dp_qlbs_oneset_m3_ex3_v4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitted Q-iteration\n",
    "\n",
    "Welcome to your 3rd assignment in Reinforcement Learning in Finance. In this exercise you will take the most popular extension of Q-Learning to a batch RL setting called Fitted Q-Iteration.\n",
    "\n",
    "**Instructions:**\n",
    "- You will be using Python 3.\n",
    "- Avoid using for-loops and while-loops, unless you are explicitly told to do so.\n",
    "- Do not modify the (# GRADED FUNCTION [function name]) comment in some cells. Your work would not be graded if you change this. Each cell containing that comment should only contain one function.\n",
    "- After coding your function, run the cell right below it to check if your result is correct.\n",
    "- When encountering **```# dummy code - remove```** please replace this code with your own \n",
    "\n",
    "**After this assignment you will:**\n",
    " - Setup inputs for batch-RL model\n",
    " - Implement Fitted Q-Iteration\n",
    "\n",
    "Let's get started!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About iPython Notebooks ##\n",
    "\n",
    "iPython Notebooks are interactive coding environments embedded in a webpage. You will be using iPython notebooks in this class. You only need to write code between the ### START CODE HERE ### and ### END CODE HERE ### comments. After writing your code, you can run the cell by either pressing \"SHIFT\"+\"ENTER\" or by clicking on \"Run Cell\" (denoted by a play symbol) in the upper bar of the notebook. \n",
    "\n",
    "We will often specify \"(≈ X lines of code)\" in the comments to tell you about how much code you need to write. It is just a rough estimate, so don't feel bad if your code is longer or shorter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import norm\n",
    "import random\n",
    "\n",
    "import sys\n",
    "\n",
    "sys.path.append(\"..\")\n",
    "import grading\n",
    "\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### ONLY FOR GRADING. DO NOT EDIT ###\n",
    "submissions=dict()\n",
    "assignment_key=\"0jn7tioiEeiBAA49aGvLAg\" \n",
    "all_parts=[\"wrZFS\",\"yqg6m\",\"KY5p8\",\"BsRWi\",\"pWxky\"]\n",
    "### ONLY FOR GRADING. DO NOT EDIT ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "COURSERA_TOKEN = '' # the key provided to the Student under his/her email on submission page\n",
    "COURSERA_EMAIL = '' # the email"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters for MC simulation of stock prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S0 = 100      # initial stock price\n",
    "mu = 0.05     # drift\n",
    "sigma = 0.15  # volatility\n",
    "r = 0.03      # risk-free rate\n",
    "M = 1         # maturity\n",
    "T = 6        # number of time steps\n",
    "\n",
    "N_MC = 10000 # 10000 # 50000   # number of paths\n",
    "\n",
    "delta_t = M / T                # time interval\n",
    "gamma = np.exp(- r * delta_t)  # discount factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Black-Sholes Simulation\n",
    "Simulate $N_{MC}$ stock price sample paths with $T$ steps by the classical Black-Sholes formula.\n",
    "\n",
    "$$dS_t=\\mu S_tdt+\\sigma S_tdW_t\\quad\\quad S_{t+1}=S_te^{\\left(\\mu-\\frac{1}{2}\\sigma^2\\right)\\Delta t+\\sigma\\sqrt{\\Delta t}Z}$$\n",
    "\n",
    "where $Z$ is a standard normal random variable.\n",
    "\n",
    "Based on simulated stock price $S_t$ paths, compute state variable $X_t$ by the following relation.\n",
    "\n",
    "$$X_t=-\\left(\\mu-\\frac{1}{2}\\sigma^2\\right)t\\Delta t+\\log S_t$$\n",
    "\n",
    "Also compute\n",
    "\n",
    "$$\\Delta S_t=S_{t+1}-e^{r\\Delta t}S_t\\quad\\quad \\Delta\\hat{S}_t=\\Delta S_t-\\Delta\\bar{S}_t\\quad\\quad t=0,...,T-1$$\n",
    "\n",
    "where $\\Delta\\bar{S}_t$ is the sample mean of all values of $\\Delta S_t$.\n",
    "\n",
    "Plots of 5 stock price $S_t$ and state variable $X_t$ paths are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Time Cost: 0.047011375427246094 seconds\n"
     ]
    },
    {
     "data": {
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av7oZKSVNxvo2PX5O7vIZrzNw/dJPOpV/R4W+d4d1nU9Y62HZYqjcC9f8C0Ze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\nr1AoFP0cJfQKhULRz1FCr1AoFP2c/w+Na9knY+5rvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0685e5f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OQgjqykoo2Lyewq0bMbU0o/HzJ+XiMaSPm0BsWmaPTd21FRfTuPRVjJ9+CpKE7rrrCJs3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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0683704898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a dataset \n",
    "\n",
    "starttime = time.time()\n",
    "np.random.seed(42) # Fix random seed\n",
    "# stock price\n",
    "S = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "S.loc[:,0] = S0\n",
    "\n",
    "# standard normal random numbers\n",
    "RN = pd.DataFrame(np.random.randn(N_MC,T), index=range(1, N_MC+1), columns=range(1, T+1))\n",
    "\n",
    "for t in range(1, T+1):\n",
    "    S.loc[:,t] = S.loc[:,t-1] * np.exp((mu - 1/2 * sigma**2) * delta_t + sigma * np.sqrt(delta_t) * RN.loc[:,t])\n",
    "\n",
    "delta_S = S.loc[:,1:T].values - np.exp(r * delta_t) * S.loc[:,0:T-1]\n",
    "delta_S_hat = delta_S.apply(lambda x: x - np.mean(x), axis=0)\n",
    "\n",
    "# state variable\n",
    "X = - (mu - 1/2 * sigma**2) * np.arange(T+1) * delta_t + np.log(S)   # delta_t here is due to their conventions\n",
    "\n",
    "endtime = time.time()\n",
    "print('\\nTime Cost:', endtime - starttime, 'seconds')\n",
    "\n",
    "# plot 10 paths\n",
    "step_size = N_MC // 10\n",
    "idx_plot = np.arange(step_size, N_MC, step_size)\n",
    "plt.plot(S.T.iloc[:, idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Stock Price Sample Paths')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(X.T.iloc[:, idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.ylabel('State Variable')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function *terminal_payoff* to compute the terminal payoff of a European put option.\n",
    "\n",
    "$$H_T\\left(S_T\\right)=\\max\\left(K-S_T,0\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def terminal_payoff(ST, K):\n",
    "    # ST   final stock price\n",
    "    # K    strike\n",
    "    payoff = max(K-ST, 0)\n",
    "    return payoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Define spline basis functions  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape =  (10000, 7)\n",
      "X_min, X_max =  4.05752797076 5.16206652917\n",
      "Number of points k =  17\n"
     ]
    },
    {
     "data": {
      "image/png": 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Kd1ORaaKhbyLIp2sAVGo46wvQcYB3jj9EzUANd266kzhN9LZ885Nu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\nD75a8uLrHfsWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0685e5ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import bspline\n",
    "import bspline.splinelab as splinelab\n",
    "\n",
    "X_min = np.min(np.min(X))\n",
    "X_max = np.max(np.max(X))\n",
    "\n",
    "print('X.shape = ', X.shape)\n",
    "print('X_min, X_max = ', X_min, X_max)\n",
    "\n",
    "p = 4              # order of spline (as-is; 3 = cubic, 4: B-spline?)\n",
    "ncolloc = 12\n",
    "\n",
    "tau = np.linspace(X_min,X_max,ncolloc)  # These are the sites to which we would like to interpolate\n",
    "\n",
    "# k is a knot vector that adds endpoints repeats as appropriate for a spline of order p\n",
    "# To get meaninful results, one should have ncolloc >= p+1\n",
    "k = splinelab.aptknt(tau, p) \n",
    "                             \n",
    "# Spline basis of order p on knots k\n",
    "basis = bspline.Bspline(k, p)        \n",
    "f = plt.figure()\n",
    "\n",
    "# B   = bspline.Bspline(k, p)     # Spline basis functions \n",
    "print('Number of points k = ', len(k))\n",
    "basis.plot()\n",
    "\n",
    "plt.savefig('Basis_functions.png', dpi=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bspline.bspline.Bspline"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(basis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 7)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.values.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make data matrices with feature values\n",
    "\n",
    "\"Features\" here are the values of basis functions at data points\n",
    "The outputs are 3D arrays of dimensions num_tSteps x num_MC x num_basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_basis =  12\n",
      "dim data_mat_t =  (7, 10000, 12)\n",
      "Computational time: 22.992000341415405 seconds\n"
     ]
    }
   ],
   "source": [
    "num_t_steps = T + 1\n",
    "num_basis =  ncolloc # len(k) #\n",
    "\n",
    "data_mat_t = np.zeros((num_t_steps, N_MC,num_basis ))\n",
    "\n",
    "print('num_basis = ', num_basis)\n",
    "print('dim data_mat_t = ', data_mat_t.shape)\n",
    "\n",
    "# fill it, expand function in finite dimensional space\n",
    "# in neural network the basis is the neural network itself\n",
    "t_0 = time.time()\n",
    "for i in np.arange(num_t_steps):\n",
    "    x = X.values[:,i]\n",
    "    data_mat_t[i,:,:] = np.array([ basis(el) for el in x ])\n",
    " \n",
    "t_end = time.time()\n",
    "print('Computational time:', t_end - t_0, 'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# save these data matrices for future re-use\n",
    "np.save('data_mat_m=r_A_%d' % N_MC, data_mat_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 10000, 12)\n",
      "17\n"
     ]
    }
   ],
   "source": [
    "print(data_mat_t.shape)  # shape num_steps x N_MC x num_basis\n",
    "print(len(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Programming solution for QLBS \n",
    "\n",
    "The MDP problem in this case is to solve the following Bellman optimality equation for the action-value function.\n",
    "\n",
    "$$Q_t^\\star\\left(x,a\\right)=\\mathbb{E}_t\\left[R_t\\left(X_t,a_t,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\space|\\space X_t=x,a_t=a\\right],\\space\\space t=0,...,T-1,\\quad\\gamma=e^{-r\\Delta t}$$\n",
    "\n",
    "where $R_t\\left(X_t,a_t,X_{t+1}\\right)$ is the one-step time-dependent random reward and $a_t\\left(X_t\\right)$ is the action (hedge).\n",
    "\n",
    "Detailed steps of solving this equation by Dynamic Programming are illustrated below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this set of basis functions $\\left\\{\\Phi_n\\left(X_t^k\\right)\\right\\}_{n=1}^N$, expand the optimal action (hedge) $a_t^\\star\\left(X_t\\right)$ and optimal Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ in basis functions with time-dependent coefficients.\n",
    "$$a_t^\\star\\left(X_t\\right)=\\sum_n^N{\\phi_{nt}\\Phi_n\\left(X_t\\right)}\\quad\\quad Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\sum_n^N{\\omega_{nt}\\Phi_n\\left(X_t\\right)}$$\n",
    "\n",
    "Coefficients $\\phi_{nt}$ and $\\omega_{nt}$ are computed recursively backward in time for $t=T−1,...,0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coefficients for expansions of the optimal action $a_t^\\star\\left(X_t\\right)$ are solved by\n",
    "\n",
    "$$\\phi_t=\\mathbf A_t^{-1}\\mathbf B_t$$\n",
    "\n",
    "where $\\mathbf A_t$ and $\\mathbf B_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$A_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\Phi_m\\left(X_t^k\\right)\\left(\\Delta\\hat{S}_t^k\\right)^2}\\quad\\quad B_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\left[\\hat\\Pi_{t+1}^k\\Delta\\hat{S}_t^k+\\frac{1}{2\\gamma\\lambda}\\Delta S_t^k\\right]}$$\n",
    "\n",
    "Define function *function_A* and *function_B* to compute the value of matrix $\\mathbf A_t$ and vector $\\mathbf B_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the option strike and risk aversion parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "risk_lambda = 0.001 # 0.001 # 0.0001            # risk aversion\n",
    "K = 100 # \n",
    "\n",
    "# Note that we set coef=0 below in function function_B_vec. This correspond to a pure risk-based hedging"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Implement functions to compute optimal hedges\n",
    "\n",
    "**Instructions:** Copy-paste implementations from the previous assignment, i.e. QLBS as these are the same functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# functions to compute optimal hedges\n",
    "def function_A_vec(t, delta_S_hat, data_mat, reg_param):\n",
    "    \"\"\"\n",
    "    function_A_vec - compute the matrix A_{nm} from Eq. (52) (with a regularization!)\n",
    "    Eq. (52) in QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    Arguments:\n",
    "    t - time index, a scalar, an index into time axis of data_mat\n",
    "    delta_S_hat - pandas.DataFrame of dimension N_MC x T\n",
    "    data_mat - pandas.DataFrame of dimension T x N_MC x num_basis\n",
    "    reg_param - a scalar, regularization parameter\n",
    "    \n",
    "    Return:\n",
    "    - np.array, i.e. matrix A_{nm} of dimension num_basis x num_basis\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 5-6 lines of code)\n",
    "    # A_mat = your code goes here ...\n",
    "    X_mat = data_mat[t, :, :]\n",
    "    num_basis_funcs = X_mat.shape[1]\n",
    "    this_dS = delta_S_hat.loc[:, t]\n",
    "    hat_dS2 = (this_dS ** 2).reshape(-1, 1)\n",
    "    A_mat = np.dot(X_mat.T, X_mat * hat_dS2) + reg_param * np.eye(num_basis_funcs)\n",
    "    ### END CODE HERE ###\n",
    "    return A_mat\n",
    "\n",
    "def function_B_vec(t,\n",
    "                   Pi_hat, \n",
    "                   delta_S_hat=delta_S_hat,\n",
    "                   S=S,\n",
    "                   data_mat=data_mat_t,\n",
    "                   gamma=gamma,\n",
    "                   risk_lambda=risk_lambda):\n",
    "    \"\"\"\n",
    "    function_B_vec - compute vector B_{n} from Eq. (52) QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    Arguments:\n",
    "    t - time index, a scalar, an index into time axis of delta_S_hat\n",
    "    Pi_hat - pandas.DataFrame of dimension N_MC x T of portfolio values \n",
    "    delta_S_hat - pandas.DataFrame of dimension N_MC x T\n",
    "    S - pandas.DataFrame of simulated stock prices\n",
    "    data_mat - pandas.DataFrame of dimension T x N_MC x num_basis\n",
    "    gamma - one time-step discount factor $exp(-r \\delta t)$\n",
    "    risk_lambda - risk aversion coefficient, a small positive number\n",
    "    \n",
    "    Return:\n",
    "    B_vec - np.array() of dimension num_basis x 1\n",
    "    \"\"\"\n",
    "    # coef = 1.0/(2 * gamma * risk_lambda)\n",
    "    # override it by zero to have pure risk hedge\n",
    "    coef = 0. # keep it\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 3-4 lines of code)\n",
    "    # B_vec = your code goes here ...\n",
    "    tmp = Pi_hat.loc[:,t+1] * delta_S_hat.loc[:, t]\n",
    "    X_mat = data_mat[t, :, :]  # matrix of dimension N_MC x num_basis\n",
    "    B_vec = np.dot(X_mat.T, tmp)\n",
    "    ### END CODE HERE ###\n",
    "  \n",
    "    return B_vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute optimal hedge and portfolio value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_A* and *function_B* for $t=T-1,...,0$ together with basis function $\\Phi_n\\left(X_t\\right)$ to compute optimal action $a_t^\\star\\left(X_t\\right)=\\sum_n^N{\\phi_{nt}\\Phi_n\\left(X_t\\right)}$ backward recursively with terminal condition $a_T^\\star\\left(X_T\\right)=0$.\n",
    "\n",
    "Once the optimal hedge $a_t^\\star\\left(X_t\\right)$ is computed, the portfolio value $\\Pi_t$ could also be computed backward recursively by \n",
    "\n",
    "$$\\Pi_t=\\gamma\\left[\\Pi_{t+1}-a_t^\\star\\Delta S_t\\right]\\quad t=T-1,...,0$$\n",
    "\n",
    "together with the terminal condition $\\Pi_T=H_T\\left(S_T\\right)=\\max\\left(K-S_T,0\\right)$ for a European put option.\n",
    "\n",
    "Also compute $\\hat{\\Pi}_t=\\Pi_t-\\bar{\\Pi}_t$, where $\\bar{\\Pi}_t$ is the sample mean of all values of $\\Pi_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computational time: 0.11096453666687012 seconds\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/ipykernel/__main__.py:21: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n"
     ]
    }
   ],
   "source": [
    "starttime = time.time()\n",
    "\n",
    "# portfolio value\n",
    "Pi = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi.iloc[:,-1] = S.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_hat = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_hat.iloc[:,-1] = Pi.iloc[:,-1] - np.mean(Pi.iloc[:,-1])\n",
    "\n",
    "# optimal hedge\n",
    "a = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a.iloc[:,-1] = 0\n",
    "\n",
    "reg_param = 1e-3\n",
    "for t in range(T-1, -1, -1):\n",
    "    A_mat = function_A_vec(t, delta_S_hat, data_mat_t, reg_param)\n",
    "    B_vec = function_B_vec(t, Pi_hat, delta_S_hat, S, data_mat_t)\n",
    "\n",
    "    # print ('t =  A_mat.shape = B_vec.shape = ', t, A_mat.shape, B_vec.shape)\n",
    "    phi = np.dot(np.linalg.inv(A_mat), B_vec)\n",
    "\n",
    "    a.loc[:,t] = np.dot(data_mat_t[t,:,:],phi)\n",
    "    Pi.loc[:,t] = gamma * (Pi.loc[:,t+1] - a.loc[:,t] * delta_S.loc[:,t])\n",
    "    Pi_hat.loc[:,t] = Pi.loc[:,t] - np.mean(Pi.loc[:,t])\n",
    "\n",
    "a = a.astype('float')\n",
    "Pi = Pi.astype('float')\n",
    "Pi_hat = Pi_hat.astype('float')\n",
    "endtime = time.time()\n",
    "print('Computational time:', endtime - starttime, 'seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots of 5 optimal hedge $a_t^\\star$ and portfolio value $\\Pi_t$ paths are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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w4m62gddXJ3BaHOZLT47Jp5vOzk5WrFhBcnIyw0foyc39mMSEOzEY4mDjQxAY\nA2PmHnRNbm4N0QhypsSdtHEdDydqAloGzAee8r9/emgF4ftf9S9gj5TyHyfY3+lPwx745KdQkw8Z\nV8Clf4egfjiFwkb4zEFvXgqLr4Q7v4Cw4SdvvKcx0uuleu9uCtcfnG0zY8b5pM+YybD00ccUtiml\nxG6vxtK2FYtlC21teQihJsQ8iZDQyYSYJ6HXR/ZvbFJS/+c/Y3n/fcLvu4+Ihx48+kVnMG/vfpun\ntzzNpJhJPDfjWQytaqyFDbgarD5h3y3ou20CAjThRjTRJoxjItBGm9DGBqCNPvmbq69YsQKn08ll\nl11GaekfUKtNJCc/APW7oeQ7uPBx0BzYPEZKSUtJO5EqQcJxppc+WZyoAngKeF8IcTdQDtwAIISI\nA16TUl4KTAfmATuEENv81/1OSvnFCfZ9euFxw4bnYdVToA+C696A0dccfdbfF5GpfsfwZQeUQMjR\nH5XPBro3Sd+zbhV7N6ylo7mxV7bNmSSPHX/EbJsH2vDS1VWExbKlR+g7HHUAaDRBmM0TkF4PtXUf\nUlW9BACTaQQhIZMICZlMaMhk32zwR8ZY/+T/0vrue4TfczeR//WzQc8KORh4nR5cDVa+yP2E+pK9\n/FP1B1Lrh9O+qoD2bkGvEmgiDGhjTBiz/YI+OgBNhPGkzvKPRHl5Odu2bWPGjBloteU0Na1gxIhH\n0WpDYdPjoDEetPALYFdNOzFWiSE+ELX21I/5xzghBSClbAYu6uN8DXCp/3gdcPb9dfemfpdv1l+7\nDTKvhkuf8Tl2T4To0TDvY1h8lc8cdMcXPj/BWUprXY0/bHMNLdWVPdk2z71lPikTp6AzHDlfjNfr\noL1jJxbLgRm+2+1zU+l10ZhDJvqEu3kigYGpCKH2X+eio3M3ltbNWCxbaGj4gpqa/wBgMAwjJGQS\noSGTCQmZjNGYhBDCt67g6b/SumQJYfPnE/mLX5zxwt/r8OD2z+RdDb7ZvKvBiqfVDhImkcwEkYg+\nMgBtfADaCdFookxoo01owgdH0PeFx+Nh+fLlmM1mzj33XHbsvB2dLpLEhDuhswEK3ofxt4Hp4DQP\nq/NrCPWqGD2h/9lKTzbKSuCTiccF656F1X8FgxmuXwyjB3BJf9x4uG0pvHU1vHWVzzF8oorlNKKz\ntYV9G9eyZ/2BTdKHZYxhwpwrST1n+hGzbbrdHbS15fsEfttW2tu34/U6AN9MPipytn82PxGDIeGI\nAlql0mKpop6+AAAgAElEQVQOHos5eCxJSQuQ0kNn514sllxaLVtobl5NXd3HAOh0UYSETEKT14Hr\n6w1E3jaPqMd+c0YJf6/d7RPwfkHfbbrxWBwHKqkF2kgTmmEmVoflscq2nslZM7hjxj2oNIO3N+6x\nsHnzZhoaGrjpppvo6FhPW9tW0lL/B7XaBFueA4/joIVf3ezd1kgakDkEsn8eiqIAThZ1O3yz/roC\nn0Nozt8goH+rEKWUWK0laLWhaLVhfQuLhMlw6/vw9nWw5GqY/9lhM5AzCXuXf5P0daup3LXjwCbp\nt91F2tRzCY44XAE6HI1Y2rb4ZveWPDo69wBehFATFDiaYfG3YQ7JIcQ8EZ3u+FeKCqEmKCiToKBM\nEhLu6Pn9Wi25WFpzaa5eiTuhCx4Hi/YTGndUERI6hZCQSQQFZvQ8WQx1vFYXrkYbrvquA47YBiue\nNueBShoV2kgjuuRgn9kmyoQmyoQmzEinp5NHVj7CVtdWfjPtN9yWedvg3cwx0tbWxvfff09qaiqp\nqSPJ3fJzjMYk4uJuAJcNtrwGqXMgYuTB11ldqBscSJMOc1T/spaeChQFMNC4nbD277D2GTCGwY1v\n+5y9/cDjsVJb+zGVVW9htRYDPtuz0ZiMyZSMyZiM0f9uMiWhTZ4BN70D790Eb1/r8w8YhkaukYHA\n5XRQmreFwvWr2P+Db5P0kJjYgzZJ70ZKic1W1mPOsbRtwWarAEClMmI2j2N48kOEhEwkOHgcGs3J\ncxoKIQgIGElAwEj0H7eiWvgVAfOuRHPHVNr8voXGpm8BUKsDCQmZ6PchTCIoKAtVPzNdDjSeLleP\nuab3rN7bcUDQC60KTZQJ/YgQNH5Br402oQ41IPpId9Bka+KBFQ9Q3FrMU+c+xWUjTo/01l9//TVS\nSubMmUN9/Wd0de1jzOjnfb/RD++AtfmwhV8AqwsbSHSpiB4TOiSf9hQFMJDUbPOt5q3f6VvMNfup\nfs3GbbZKqqqWUFP7AW53O0FBY0hL+xNerwOrtQybtYy2th+or/+cA+EQoNGYfYrh4oswFq7B9Mls\nTBc/i9GciVZ7bJuODDW8Hg/lO7ZRuG4VRVs24bLbCAgNY+xPLiNj+kyiU0YhhMDrddPevsPvrN1K\nW9tWnM4mALTaMELMOcTH3+qfZWcOilBtevllmhYuJOTaucT+9k8IlYr4eF9+eLu9xq+scmm15NLc\nvAroVlbje5zKwcFjUatPTly7p9N5sI3e/+7tdPXUETqfoDeMCvHZ5qMD0EaZUIfo+xT0fVHZUcl9\n395Hk62Jf170T2bEzzgp9zPQFBcXs3v3bi688ELMZhO79zxLUNBooqIu9aVv2fgixI6F5MPvZ/OW\nWuIQjJ88dFb/9kZRAAOB2wFr/gZr/wEBkXDzv305fI4BKSWtlk1UVS6msek7hBBERs7GaLycwj0O\nNm3cz/Dhw8nJuYT0NF9kidfrwGarxGotw2orw2Yrx2otw+Iooy7JBDRAgS+PjFYbhtGYhMmUdMiT\nQzIazclLbXA8SCmp2VdI4fpV7N24Dlt7G3pTAGlTzyVjxkyGZY5BSift7dspK1voE/jtP+DxdAE+\nx2tY2AxCzD6nrcl06mP7D6Xp1VdpfO55zFddSeyf/uewsFODIY6YmCuJifHl+nc6m7BYttJq8TmW\n9+9/nv1IhNARHJzd41Q2mycc89OLlBJvlwt3ix13sx13kw1Ps8133GzDa3X31BV6NdooE4b0MJ/Z\nxj+rV5uPXdD3xd6Wvdy/4n5cXhev/eQ1siOzj7utU4nL5eKLL74gPDycadOmUVW9BLu9mvT0JxFC\nBcXfQtNeuPbVwyL6vF5JU7GFWKEiMX1ommUVBXCiVOf7bP2Ne2DsLTD7STAePdbX47FRV7+MqsrF\ndHbtRasNIz7+blqas1i3toL6+g2ohMCIh/yWZvLy8gjQqIkLCSYhMpyAwCB0JiN6UwYGYw7mQBO6\nKBNavQpPyfu4Nj+JLSENa9oMbPZKWls3UVf3yUFj0GrDe5mUknoUg9GYfFJNI4fSWFFG4bpVFG5Y\nQ3tjAxqtjhETp5AxfSbxo1Po7NqOpe1L8vL/REfHTqR0AYLAgFRiYq7xmU7MEzEYhlYUVPMbb9L4\n938QfPnlxD75JEJ9dBu/ThdBVNRsoqJmA+BytfmfbnKxWLZQXrGIsvIX/f6GMT2hp+bgHNR2I+4m\nO+6WA8K9W+BLh+dAJwLUZj2acAPGMRFoIv0RN9Em1MG6AVeaW+u28vDKhwnQBvCv2f9iRMiIAW3/\nZLJ+/XpaWlqYN28eYKOs7EVCQ6cRHuaf7W9cCEFxvui+Q9hZ00a0FfQxRnTGoSlqh+aoTgdcdlj9\nFKz/PwiMhls+gNSfHPUyu72Gqqq3qa75D263hcCAdMLDf0HRvhBWryrB49mCQUgMdZVo2pqJHJaA\n0Gpp9Qg6NHqK3B6KGprQtLeiszSisnX1GWMrxDnohBOdfhf6iAR0xmnoA3XozW60QXa0AV149e10\nOVrpaCvGS9tB12s14RhNyQQEDMdkHO5XDL4nCbXadMJfX1tDnW+T9HWraK6qQKhUJGeP55zr5xA6\nXNJpLaCp7QnKNxX570dHcHAWiQl3ERIyCbN5Alrt0PVztLy1hIannyZozmzinvrfYxL+faHVmomM\nuIjIiIuQXomzpYWW2lwsllzaLflUtr1JRcVrIAX6jmEYW9MwWdIwWtIwBEahDjdiSgzyLZoKN/je\nwwynLLRyZcVKfrX6V8QHxbPo4kXEBg4tJf1jtLS0sHbtWkaPHk1KSgqlpc/hcrUwMuVXvgp1O6F0\nFVz8xEELv7pZtb2OaI+K9HFDL/yzG0UBHA9VW32z/qa9vrjfn/wFjCFHrC6lxNK21W/m+QYpJSEh\nF9BmyWHDhi7a2hrQiAY0lib0zfWEBgeRcf4FZJx7/mEOzpqaGrZu3crOnTuxhkQQFhJC6vBkkqIj\nwePGabXitFlxWK04y3Jxlm7C4dHi1KZhtVix1FpxWLtw2my4nQ5AD8Sh0sSgC3aiN/d+7UZv3o7W\n5D7ofrxOI9IZgsoTjlpEoVXFoNcNw6BPwBAQgs5oQm80oTOZ0JsC0BmNaHR6rG0W9m5cR+H6VdQW\n7QUkiROGkT47C2NkBx1d39HgeJuGYr9T1DyBmOgrMZsnEhycfdJs4ANNy7vvUv/kkwTNmkX8X/+K\n6Md+AdLjxdPqODB77/3eYgePBAIJ4kKCNBehClfhjK3EFrKXzpCdtJvXYpErADCZUvxrEaZgDJmE\nwTCwufCPxsdFH/PExicYHT6aFy56gVDD0FoF+2NIKfniiy9Qq9VccsklOJxNVFT+i6ioSwkO9puv\nNr0IWhPk3NFnG4XbGhgNpI9XFMCZgcvmy9+zcSEExcKtH8KoI6ZKwuNxUN/wGVWVb9HRuQuNxozR\neBWlJQmsXdMC1KJzWDE01hLgcZF2zjQyz73/iDtLCSGIj48nPj6e2bNns3PnTvLy8tj0wza2qNVk\nZmaSk5NDUlKS/zF+Hmz4J3zzBxgTCVe/BL3a9bjdOO02nNYun8KwWXHabH4F4VcinVYcjRZcnlo8\nNOBVNYOuFZWhA42pEWHYiQNwAO0SnHUaHG26g17ejkDSNLOIM6SgDi5lZLyb5PFanMGleNSFdAHO\n5jCC1GOJNdyE2ZRDYFAqKqMelUGDyqAZMiGSUko21m7E7XUzLW4aGtXB/4Va//M+9f/zJwIvvJD4\nvz+D0B7udJYuby8zTbeQ9332WOw9eW3A73wNN/rs8pnhB2bx4UafuUZ1qN3ZSUfHLl/oqSWX+vrP\nqan5NwAGQ0KPDyEkZBJGY+JJ8ZFIKXlj1xs8m/cs0+Km8ez5z2LSnvhT46lkz549FBcXc8kllxAc\nHMzefU/g9TpIGfGor0JHnW/h18Q7+zT5tnQ5EfV2pF5HxLDAUzz6Y0dRAMdKZa5v1t9c5NP4s/4E\nhr4jbByOeqqq36G6+j1crhb0+uG4XDeRt9WI1epG421E11yHvqOVEWOyybzyPlJyJqPRHf4YeST0\nej05OTnk5ORQW1tLfn4+BQUF7Nixg/DwcCZMmMDYsWMJnPawz1z1/Z9Ba4DLn+txVqk1GoyBQSeU\n597t7qCjo4jOtmI6O0qwBpZhD63E6a7GKy099TxyL5VSDSrf04TOGUeQZTJGyyiMjSPRtEcg/MYs\nO27sfWwXIfRqn0IwqhF+xaAyahAG9QFFYTxwfFjZCSzD7xb8C39YyI6mHQBEmaK4ZuQ1XDvqWuIC\n47B8+CF1/+//EThzJrFPP4OryYm7uR13sw1Pi88W726242l39A7iQhjUaCKM6BKC0IyN9An4CJ+g\nVwVq+yWkVSodZvN4zObxkHQfUnro6NzjC4m15NLUvJLaug8B0OtjCAmZRFLS/QQFph/3d9Mbr/Ty\nj63/YPHuxcxJnsNfZvwFrXpww1n7i8Ph4KuvviI6OprJkydjs1VQXf1vYmOvx2Ty593KfRW8bphy\nf59trNnXQLJLTdTokBNynp9shJRDN+PyxIkT5datWwd3EE4rfP8X2PgCmIfBlf8HKRf2WbWt7Qcq\nqxbT0PAlUnrQaCZQtj+F/ft1CEDd3orW0kR8bAyjz72AtGnnYQoeODu20+lk9+7d5OXlUVlZiUql\nIj09nZycHIbvfxvVun/4/mBnP3V8OYj6gauui6Zl2+hsKkYmtqMa60AaXZiDJ2AOyUGvOyTTo8eL\n1+5B2t14be4Dx3Y3XpsHr93dd5ndg9fmK+Nof8oa0UtRaFAdQXEIowaVXo3K6FMiuzr28NLeRWxs\n2kxMYAz3j70fs87M57s/paK8lFhnJFc0pTGqWKCNTUEdOuygEEoAVYC21+zdgCbCiDrML+RNmlMW\nreTLc1SMxbKFVstmWlrWIaWL0aOfIzLisKwu/cLldfHEhidYVrKMm9Nv5rHJj/Vr4/ahwrfffsv6\n9eu56667SExMZOeun9PY+A3Tpq5Er4/2yYRnMyFpum/9TR889upWEvLaueiODNLPObV+DyFEnpTy\nmHbQUZ4Afozyjb64/pYSmHg3zPpvXyK3Xni9ThoavqSyajHt7dtRqQKw2aaya0ckVlsAaocNfWsl\nYVo1Y2acR8a5FxAWN+ykDFen0zFu3DjGjRtHQ0MD+fn5bN++nd27dxMSEsKEhIcZt/l1gjUGn+Pq\nJAgdr8ND+3fldK6rRmXQEDfnEkw50UedBQm1CnWACgKOb7YopUQ6PT7lYDugHA4cH/rZd+yyOHqU\nDG5vn21HAI9zO5J5PiVRrEE6PaRZrz+oniOmlX0hbegj60ieOJKwuOgega8yDI3/akKoCAxMJTAw\nlWHDbsXhqGd7wQIKCu5j1MjfkpBw13EpI5vbxi9X/5I1VWt4aNxDLMheMOghuMdDQ0MDGzduZPz4\n8SQmJtLRsZv6+mUkJd3vE/4A298DW2ufC7/AF/7ZsM9CAioSB3gP4oFmaPxVDjWcXfDdn2Dzy74c\n/LcvgxEzD6ricDZRXf0u1dXv4nQ2AjFUVZ5LeXk80q1C09ZMiL2BjAk5jL59HvFpfdv1j0Sbo42d\nTTspay/jvGHnHdPGGL2Jiopi9uzZXHTRRRQWFpKXl8fKMgvfcy+p60vIaX+Skdf8FlU/xvRjSCmx\n72rG8lkJnjYnAZNiCJ6djPo4BXp/EUIg9BpUeg2Yj2/HJen24rW72V9fwtId77O7eieR6gguib6Y\niaETUDsF0v/E0W2bd5btpumFv6FPT6Di9zfyceVm1lavRdZLpqmnMdc8l/N15zNU58F6fTQ5E95j\n1+5fUlT8JF3WUtJSn+jXgrk2RxsPffcQ2xu38/g5j3ND2g0nccQnDykly5cvR6/Xc/HFPt9eSekz\naDRmkhLv81Xyen3O37gJkDi1z3YKqtuItkq0kXpMwcdu1h0MFAVwKGXrfLP+1jKYvAAu+n+gP+DE\naW8voLJqMfX1y5HShc06kuKSbCytsai7OtC31zAqZQRjLruVEeMnHZNd3+P1UGwppqCpgO0N2ylo\nKmB/2/6e8qdzn+aChAuYlzmPnOicfs2stFotWVlZZGVl0dzcTH5eHttyJXt3uAje9yfGn3Me48eP\nJyTkyFFMR8PdbMOyrAT73la0MQGE3ZKBPun0W4FcYa3khW0v8NX+rwjQBjB/xnxuy7iNQF3fTrz2\nr7+h4elHMY0fT8JLC0k2mbgg9RLquur4uOhjPiz6kEdXPUq4IZyrR17N3FFzSQgeemm71WoTWWMW\nUlL6d8rLX8ZmqyBrzMJjCrOt76rn/hX3U95ezjMzn+EnyUcPhR6qFBQUUF5ezhVXXEFAQACtrZtp\nbl7NyJTfHFhRX/QNNBfD3H8d8Qn6+x11xHlUpGYP/cSMig+gG0cnrHgCtrwKocPhqoU9S7u9XheN\njV9TWbWYtrZ8pNRTX5dCVdUo7O0GtG1NxIUEM+7cC0idOuOodv1mWzM7mnawvXE7BY0F7GzaidVt\nBSDMEEZ2RDbZkb5XbEAsnxR/wgf7PsDisJARlsG8zHnMTp593M41t8vJvrceJa+ykxKSARg5ciQ5\nOTmkpqaiPsaYden20rGmivaVlQiVIHhWEoHT4hDq0+vRv6azhpe3v8yykmXo1DpuSb+FO8fciVl/\n5N+x47vvqPrZf2HMzibhlVdQBx6+cM7j9bC+Zj0f7PuANVVr8Eov58Sew3Wp13FhwoVD0jlaU7OU\nwr1/wGhMZGz2q5hMSUesW9ZWxn3f3ofFYeH/Lvw/psROOYUjHVhsNhsLFy4kJCSEu+++GyEEW/Ou\nw+GoY+o53x0IQX7zcmjZDz/bBkf4/e59cg3jKtxc84vxxI069aGv/fEBKAoAoHQ1LHsILJU+J+lF\nj4MuAKezmZqa/1BZ9TZOZz1Oh5nKylHU141AWLow42H8lKmMPu8CQmP73kfW5XGxr3Uf2xq3UdBY\nQEFjAVWdVQBohIa0sLQeYT82cizDAof1OcO3u+18Xvo5b+9+m5K2EiKMEdyYdiM3pN1AmOE4lpl7\nXPDBHbQWruGHUY/yQ52Xjo4OAgMDGTduHBMmTCAs7Mjt2ostWD4txt1ow5gVgfnyEWiO0/QyWDRa\nG3ml4BWWFi1FhYob0m7g7qy7D9uK8FA6vv+eqkd+hjEzk4R/vYY68OhhfvVd9Xxc/DEfFX1EbVct\nYYYwrhp5FXNHzSUp+MhCdjBobd1MwY6fIoQgK+slQkMmHVZnV9MuHljxAEIIXrz4RUaHjx6EkQ4c\ny5cvZ+vWrSxYsIDY2FgaGr9mx46fkpH+v76MnwC122HReb4IwOmP9NlOU6eD3/1uNdleLQ88PxO1\n+tQb/xQFcKw4OuDbP8LW1yEsBa56AZKm0tGxh8qqN6mr+xQpXbS2xlJTnY6lNgyjtYPRGRmMPf9i\n4tIyDhPW9V31B5lydjfvxuHx5UOPMkYxNmpszww/MzwTg6Z/i5uklGys2ciSPUtYV70OnUrH5SmX\nc1vGbYwK7ef+wG4n/OdWKPoWz1UvUWyaQF5eHkVFRUgp/TmIckhPT0fjX8zk6XBiWV6KbVsj6jAD\noVelYEgbmnlOjkSrvZXXd77Oe4Xv4fF6uGbUNSzIXkBMwNETdnWsXEnVz/4LQ1oaiW+8jjqofyG0\nHq+HjbUbWbpvKasqV+GRHibHTOa61Ou4KPEidOqhYTO2WvezveBebLYqMtKfJDb22p6yTbWb+NnK\nnxFqCGXRrEVDToH1l5qaGl555RWmTJnCnDlz8HrdbM69FIApk79A1b3W46P7oPBz+PmuIy78/DCv\nkr2v7WVEahg3/XzCqbqFg1AUwLFQ8j0sexjaqmDqg3jP/w1NbRspK/8XHR15eDwaGupHUFM5Cle9\nl+Gx0UyceSEjciaj8S/ucXgc7Gnew/bG7T3mnHprPQA6lY7M8MyDZvfHImD6Q2lbKe/sfodlJcuw\ne+ycE3sO8zLnMSN+xrGH37ns8O4NULbWZ9cccy1tbW1s27aN/Px82traMJlMjM0eS7o6Ac06C9Lt\nJej8BILPH4bQDo0FWsdCu7Odt3a9xZLdS7B77Fw+4nLuz77/mO3y7d98Q/Wjv8AwOpPEV19FHXxi\nfo5GayOfFH/Ch0UfUt1ZTYg+hKtSrmJu6lyGmwd/n2eXy8KOHQ/SatlEctIDjBjxKN+Uf8tv1/6W\npOAkFs1aRJRp6K5yPRa8Xi+vvfYa7e3tPPTQQxgMBmpq3mdP4W/JynqRqMhLfBXba+C5LJh0L8x5\n6ojt/fJfWxm+pZ3zbk4la+bJifY7GooC+DHsbfDN45C/GMJH4brir1RRRFnZ63i9TdjtAdRUp9O4\nP5pQTQCTpk5n9IyZGAKDqO6s7hH0BY0FFLYW4vb6FjbFB8b3CPrsiGzSw9JPmY23zdHGB/s+4L3C\n92iwNpAcnMytGbdyZcqVx7YC09nl21CmKhdueAvSfTnavV4vpaWlbFm3maKyYrxIYnURTDpvCllT\nxqHtY5XrUMTqsvJu4bu8sfMN2p3t/CTpJzw47sF+JSVr//JLqn/5K5/N/9VXjsnsc6x4pZdNNZtY\nWrSU7yu+xy3dTIyeyNzUucxKmoVePXimNa/Xxd69f6Sm9n0chjE8XlzK6Mjx/PPCf/6oj+R0YcuW\nLSxfvpy5c+eSlZWFx2Nn46aL0OtjmZjzwYEn/BVPwPrn4eF8COtbOXu8kvmPrWBqu5p5f55KcMTg\nbACjKIAjUbQCPnsEOmrpnDaPojBBc+tXCJUbiyWamoqROGsjyM7KYszMmVRpmw+a3bfYWwAwaoyM\niRhzkLP2aHbjU4HL6+Lbsm9ZsnsJO5t3EqQL4rrU67gl/ZajP33Y22HJNb4dzG5+D0ZejNfmpu3r\nMro212IPkFSm2dhRu5eWlhYMBgPZ2dnk5OQQHT30troD3xPa+3vf57Udr9Fib2HmsJk8OO5BMsIz\n+tVO22efU/Ob32CcMJ6Elxf16fAdKJpsTXxa/ClL9y2lqrMKs97MFSOu4LrU60gJSTlp/f4YXq+X\n93PvIbxrNW2YmXXOJ5gDEgdlLANJZ2cnCxcuJCYmhvnz5yOEoLz8FYpLnmbC+HcJDfU7tR2dvoVf\nw2fCjUuO2F5eeSvv/m0rqYFG7ntq8PY6UBTAodgs8PXvkdvepjY5hcLYUKS2DI9HTUPDcBpLEggJ\nGo5hTDhFAfUUNO2gyFKEV/oWBiUHJx+Y3UdmMzJk5GE5YIYSUkq2N25nye4lrKhYgUAwK2kWt2Xe\nxtjIsUe+0NYKi69ANhZhnfwBbVt0eLtcBE6LI3hWEiqDBq/XS1lZGfn5+ezZswePx0N8fDw5OTmM\nHj0avX7wHcEuj4uPiz9mUcEiGqwNTImdwkPjHmJc1Lh+t9X26afU/PZ3mCZOJOHll1CZTk1OG6/0\nkluXy9J9S/mu4jvcXjcToiZwXep1zEqa1W/f0fHi8Xp4Kvcp/r3339w1fALjvHlotWbGZr9GUFD/\nFOlQ4+OPP2bHjh088MADREZG4nK1s2Hj+ZiDxzJu3BsHKua+Cl/8Eu7+1rcF6xH4+5eFqD+tZsy5\n8Vx868Ck1jgeFAXQm31f41z+CAUmFU0JWrSGLux2E3WVKbTUx1EfZWdz4F4snnYAgrRBZEVm+Wb2\nEdlkRWQRYjj+GPnBpqazhvcK3+PDfR/S4eogOzKbeRnzuDjp4j6VmKusBssbX+NwjEQXLQi5YRy6\n+L7NHV1dXRQUFJCXl0dTUxM6nY6srCxycnKIi4s72bd2GB6vh+X7l/Pithep7qxmXOQ4Hh7/MJNj\nj/yf9sewfPghtX94nICp5zDshRdQGQfnkb7Z1syykmUs3beUio4KgnRBXJlyJXNHze2/478fOD1O\nfrfud3xd9jV3jL6DR3MepbNzN9sLFuB2tw9I+ojBoqysjDfffJMZM2b0LPoqLvkb5eUvM3nSZwQF\nZfoqej2wcCKYwuGeFT/a5h3/u4ZJ5W4uezCb5KzBswgoCgDA1krtskf4wVaIJq4NtcZDmyWS6vJ4\ntnR0sSumFpdeMjJ0JNkRB2b3w83DT8v8JUfD6rLySfEnvLPnHSo6KogJiOHm9JuZO2ouZr0Zr9ND\nx8pKOtZW/X/2zju6qirtw8+5JTe990YSahJKKFKULk16E7AgoIgoWMYZR2d0xm+aOnbBhugAgg3p\nIkqTUKQTWhJIIUB67+3W/f1xk9ASIL2dZ62s2/Y5Z19I9u/styKpJRwsv8fGtBVp3hbwuX00gxCC\nxMREIiIiiIqKwmAw4OnpSd++fenRoweWlo17t2oSJnZd3cWnZz7lcsFlgp2Debb3swz2GVzncgR5\nP6wn/fXXsRk8GN+Pl6No5O9wNwghOJF+gg2xG9iTuAe9SU8vt17M7DKTsQFjsVI1nECV6Et4Yd8L\nHE07yot9X2RB9wVVn1WWjygqiqpX+Yjmwmg08vnnn6PT6ViyZAkWFhZotRkcPjISN7cxdA/94Nrg\niz/D9w/Dg6shdFqN58wsKufPr+3nHr2aRR8MQ61pvuCIdi0AZeUl/PzRn1EERuDgmonJpCAzzZeo\nVBtOO5fQMSi0ym7f3aV7jVmebRWTMHEg+QDrotdxLP0YViornrFewP0XeyEVGLHu447D+ECUxixY\n9YDZaT5/O3j2uKvzl5WVcf78eU6dOkVGRgZqtZrQ0FD69u2Lr2/1OQ51RQjBgeQDLD+9nJi8GDo6\ndGRp76Xc739/va6T++235pLOw4bhs+wjFC3ArHUzeeV5VbuCK4VXsFPbMSFoAjO7zKSrc9d6nTu3\nPJcle5ZwIfcCrw96nWmdb134jMZSoqL/RFbWTry959S6fERzcvjwYXbt2sWcOXPo1s1sqrl48TVS\n0zYwaOAurKyu82+sGm/OD3ruNChrNvtuOJVM1FcX6dzBgYdfvjVvoilp1wIQd+IwCXmPYzKq0CX3\nQZXTA6t7Q+nUMxQ/h8apf95aib0STcbmCwRmuHPVIpWDPS8w7N6xDPQaaP53yrtqFgGDFub/DO53\nb78+RH8AACAASURBVNcUQpCSkkJERATnz59Hr9fj5OSEl5cXbm5uuLu74+7ujrOz811nHl9/7mPp\nx1h+ejnnss7hZ+fHM2HP8EDAAygV9bvzyv16LRlvvIHt/ffj88H7KGpRors5EEJwKuMUG+I2sPvK\nbnQmHT1de1btCmpbhz+1OJWndj9FWkka7wx9hxH+I25zbVNV+Qgnp3vvunxEc1JQUMDHH39MYGAg\nDz/8MGDOeTh6bCw+Pg/Ttcv/XRucEgErR8DYN2os/FbJ8/87SZfjhdw7oyO9RzdvXkS7FgCAzSte\nRRl5Dz4WjrgpQaFQIqkElqFuWIW6YtnFqcVUZ2wOhNFE8aEUCvckAqAc5soW59/4Lu57cstz6eTY\nibkhcxkfOB7LghSzCCDBgh3gUvtIFK1WS2RkJLGxsWRmZpKXl1f1mUKhwNXVFXd39xuEwcnJqdpC\ndaczT7P89HJOpJ/A08aTxT0XM7nTZNQNcPeZs2q1uY3j6NHmZi4tfPG/mfzyfH5K+IkNsRtIKEjA\nRm3DhEDzruBuIp/i8+J5as9TlOnLWH7/cvp69L2r69amfERzs379emJjY1myZAlOTuYyDecjnyUn\nJ5xBg/bdWKZ840KI+RVejK6x9weAwWji4b/sYVihijl/649LDT6zpqLdCwBAUbGW/71zHMsMPf7a\nFLroMrDw6oGksgaFhKajA1bBLlgGO6Nyan77blOhTSggb0s8hsxSLENccJwUVPX9dUYdv1z+hbXR\na4nJi8FJ48SsrrOY7dIXt+8fAZWVWQSc6vcHrtPpyM7OJjMzk6ysLDIzM8nMzKSg4FpfYpVKdYMw\nlFuVsyV9CweyD+Bi5cKTPZ/kwS4PNljmbPbKlWS99z5248bh887b1Xbyai0IITideZqNcRvZeWUn\nWqOWUJdQZnaZyQOBD2CjvjWM9UzmGZbsXYKF0oLPR31eazPS3ZSPaG7i4uL45ptvGDlyJEOHDgXM\nxR1PnJxGYMCzBAW9cG1wQTJ82BMGPg1j/3Pb8564ksva904RYqHhqXeHNLuVockEQJIkZ+AHIAC4\nAswSQuTVMFYJnARShBAT7+b89Y0CEkKwZX0MyftS0Ju09E7fhE92BuqA/qgDB4LRvPCpvWywDHHB\nKtgZtY9ts/8HNgbGYh0FOy5TGpGJ0lGD4+SOWNVQq1wIwcmMk3wd/TX7k/ajVCgZ7zGIR8/tIFjt\nAAt+AfuGj/LRarVkZWXdIAppGWmUFpdWjZGUEh7uHnh6eN6wY7C3t6/z/1v2Z5+R9dEy7CdONDdw\nr0UP35ZOgbaA7Qnb2RC7gfj8eKxV1owPGs/MLjOr6vccTD7Ii+Ev4m7tzorRK/C1q1sG6+3KRzQ3\ner2eTz/9FIVCwdNPP11V2iTi9FyKiy9y76DfUKmuK+ux62/mJlDPnzGXhL8Nb++4gPKnVEL7ezJu\nQfPXRGpKAXgbyBVCvCVJ0iuAkxDi5RrGvgj0A+ybSgAqiY3K5ucV51HoTBTa5zOnYC+GA+EoHLyx\nHT4bpUcPDJl6EKCwt8Aq2BnLEBcsgxzr1UawJSBMgpIT6RT8egWhM2I3xBe7kX4oLO7OVp5YmMi3\nF79lc9xmSg2l9NXqmWu0YvijO1DaNV6no8TCRD49+yk7EnZgr7DnQe8H6Wfbj8LcwqqdQ3FxcdV4\njUZTJQjXP9rZ2dUoDEIIsj/+hOxPPsFhymS83ngDqZb+iNZCZW7IhtgN7Lyyk3JjOcHOwQzwGsC6\n6HV0durMp6M+rXdCY3XlI6QWEFUXHh5OeHg4c+fOpWNHsxkzJ/cQZ87Mo3Pn1/D3uxblhLYI3g+F\nTvfDg6tqOOM1HnlzP/deNTJmYSid+zV/UmRTCkAMMFwIkSZJkhcQLoS4Ze8oSZIvsAb4D/BiUwsA\nQGmRlnUfRqBPKSPOysT4MY70PPEL+Zs3I8rKsLlvBLajHsJkcEEbl4fQmZAsFFh2djKLQTfnJmtu\n0lDoUorJ2xKPPqkITZADjlM7oXavWyJToa6QzXGb+fb8KlK1OfiaJB7pvYSpIY80aCRVWnEaK86t\nYEv8FtQKNQ8HP8yC0AXV5mKUlpbeYkbKysqitPTajsHS0vIW/4Kbmxs2NjZkffQROZ+vwGH6dLz+\n9c82u/jfTKGukJ8TfmZD7AZi82Lp79mfj0Z81GD/j9eXj3B3e4CQkHdQKpsnhwIgNzeXTz75hODg\nYGbOnAmYHdgnTk5Fry9g0MBdKBTXRXod/Rx+fRkW/ga+t/eDZBSW8+Lf9nOvTs0T7w7BsgWsEU0p\nAPlCCMeK5xKQV/n6pnEbgDcBO+BPtxMASZIWAYsA/P39+169erXO87sZk0mw+8dY4valkK0wYRjo\nzMsPdEC7aSN569ZhyMpC07kTTo/NRxM8BG1cAWUXcjEV6kACiw72Zr9BiDNqt6bJCK0LpnIDhbuu\nUnwkFYWNGocJQViHuTWIactgMrDv5MesPfMZpzUW2KismdZ5Oo8EP1Jn0wGYC6OtPL+SDbEbAJjV\ndRYLeyys0x1pcXHxLaKQmZlJeXl51RgrScIuPR03d3cCJkzA3cMDNzc3rJso07clIITgcuFl/Oz8\nGsSJfvO5E5O+Ij7+LezsutOr5xdoNE1fOE4IwTfffENiYiJLly7FvqKAX0bGdiKjnick+F28vK4L\nczUZYVlvsPOCJ3be8fzrTyRxdnUM3bzsmPtay+iH0KACIEnSHqC6QjKvAmuuX/AlScoTQtzQAUGS\npInAeCHEM5IkDecOAnA9jVUNNOF8NjtWRqLXGYnwUPDSk73p7m5N4c87yF29Gm1MDEpXV5wfeRiH\n2bMRpWrKLuRSHp2DPq0EAJWrFZYhzlgFu2DRwf6OPW+bAiEEZeeyyd+egKlYh80ALxzGdEBh3Qh3\nJXF7iNw4l7UevuxS6jEhqrqW9XHvc9dik1+eX1WaWW/SM7XTVBb3WtzglVOFEBQVFZGZmUnC9z+Q\nFhNDaccg8iws0Ol0VeNsbW2r3TE0djJbWyUrazeRUX9otvIR0dHRrF+/nnHjxjFw4EDAvEM5emws\nCoWGAf23Y3ZPVh6wDdbPhVlrIWTyHc+/dNUJuh0rpP+EQPpPuvvigo1JizIBSZL0JjAXMACWgD2w\nSQjx6J3O35jloItyy9m4/AwlaaWc1hjoPTmQxSM6oZCg9MgRclatpuTgQSRLSxymTsF53jw0gYEY\n8sspv5BLWXQO2oQCMAoU1iosuzljFeKCprMTimbIAtRnlZK/9RLa+HzUPrY4Te2EhV/tatXXmgvb\nYf1jZPj34/vuY/jx0hYKtAV31bWsSFfE2ui1fB39NaX6UiYETeDpXk/jb994RcaEEGS88SZ5a9fi\nNHcuHn/9C2CODb95x5CVlYVer6861t7e/hb/gouLC1bNVB6iNVFUFNUs5SO0Wi2ffPIJVlZWLFq0\nqCrfJDn5G2Ji/06vnitxdR1540FfjYWiNHPi1x1ySvRGEw/+dQ+jC1TM+HNfPINaRg5EUwrAO0DO\ndU5gZyHEn28zfjgtYAdQidFgYt8PscQcTCVVaSIp2Iq3Hu2Dt6P5j1obF0fOmjUUbt2GMBiwHT4c\n5wXzsb7nHiRJwlRuoDw2zywIF3MRZQZQSlh2csQy2BxVpGzkLllCb6RwXxJF+5ORVAocxgVgM8Cr\n6XYkkRvN8dKBQyl7cA3bk3azLnodCQUJuFq5MqfrHGZ1nYWTpXljeHNp5tEdRrMkbEmjV7oUJhPp\n//oX+d99j/OCBbj/+aXb7lJMJhP5+fnVCoPRaKwaZ2Njg6urKy4uLjc8Ojo61jrBrS3THOUjdu3a\nxeHDh3niiSfw8zP3fDAaSzl8ZCRWVh3o2+f7G+eQfBK+vB/G/RcGLr7j+Y8m5LD6w1P0kix46oNh\nKFqAFQCaVgBcgPWAP3AVcxhoriRJ3sCXQojxN40fTgsSgEriTmawe000pQYTvzkaWfJQDyb0vBbh\nYsjOJu/b78j77juMeXlYhobivGAB9mPHVMWLC6NAd7WAsuhcyi7kYMwx25vVPrZVUUVqL5sG/aUv\nj8klb9sljDnlWIW54TghCKVdMyQvnfkWtjwNncfC7HWYlCpz17Lotfye+jsapYaJQRPpYN+B1VGr\nyS3PZYjPEJb2XkqIS0ijT0+YTKS//jr5P27A5cmFuL34Yp3/H0wmE7m5uWRnZ5OTk0N2dnbV8+ud\nzwqFAmdn52rFoT35Ga6nKctHZGRksGLFCnr16sWUKVOq3r9y5VMuJbxH377rcXS4ycH743yI/w1e\njALNnXfPb+24gPRTKqG93Ji4uGcDf4O6IyeC1YG89BK2fXqOoswyDlvq8bnXg9endMdWcy0m3FRe\nTsGWreSuWYPu8mVUXl44P/oojrMevKE1oBACQ1YZZdE5lEfnoEsqAgFKB02V30AT5ICkqlt4nLFA\nS/72BMrOZ6Nys8JxSicsOzVzxdKT/4Ptf4DgyTBzVVXdlEv5l1h3YR0/XfoJrVFLf8/+PNv72TqV\nZq4Lwmgk7bW/UbB5My5PL8btueca7c6ztLT0FlHIzs4mNzcXk8lUNc7a2voWUXB1dcXJyanN7xqa\nonyEEILVq1eTmZnJ0qVLsbExJ77p9Xn8fng4Tk4D6dVzxY0H5V2FZWEwaCmM+dddXefBt/Yz/IqR\nEXO7EXJf01e/rQlZAOqIXmtk3zcXiTuewRWVkTO+St5+uDe9/W/wayNMJor37yd31WpKjx9HYW2N\n44MzcZr7GBa+tzaHNxbpKL+YS9mFXHOIqd6EpFFi2cUJqxAXLLs63ZWjVhgFxYdTKNydiDAJ7Ef6\nYTfUt85C0uAc/Qx+fQV6PAjTVtxgQ80vzyezLJMuTl2abDrCaCTtr3+lYOs2XJ9dituS29dzaSyM\nRiP5+fk3iELlY0lJSdU4hUKBk5PTDaJw/a6hLSUoNmb5iLNnz7J582YmTZpE377X7vLj4t4gMWkV\nA/r/jK3tTb+HO1+FY5/D82fB4c7RbGkFZTz3+gGGl6uZ9+Z92Dq1nIKBsgDUAyEE0YdS2f99LMUI\nttlomT22E8+M6ISyGhtfWVQUuavXUPjLL2AyYTd2DC7z52PVq/rGK0JvpDw+3+w3uJCDqUgPCtAE\nOJj9BiHOqFxudSxqrxaSvzkefXoJll2dcJzcsdpxzc7B92HvP6D3ozBpOVRTz6cpEAYDqX9+mcId\nO3B74XlcF9/ZptsclJWV3SIKlbuG630NlpaWt+wYXFxccHZ2rspqbW00RvmIsrIyPv74Y5ycnHj8\n8cer6kmVl6dy5Oj9eLhPIiTk7RsPKi+E90Og6ziY8eVdXee744mc/jqGUGdb5v1zUL3n3ZDIAtAA\nZF4t5JcVkRTllfObpQ5lFzs+mNMbX6fq7bf69HRy164lf/2PmIqKsOrTB+cF87EbObLGBCNhEuhT\nis2mogs56NPNNmSVuzVWIc5YBrugcrGk4NcrlJ7MQOlggeOkjliGurTsu8F9b8D+/8I9C2H8u9DE\ncxV6PSkv/ZmiX3/F/U9/xGXhwia9fkNQ6YSuThyuz4CWJAlHR8dbdgwuLi7Y2rb8siYNXT7i559/\n5uTJkyxatAgvr2t+vOgLL5ORsY1BA/diaXmTuebIJ7Dzr/Dkvjv2vqhk8aoThBwrou8oP+6b2XhN\neeqCLAANRHmJnr2ro7lyPod4jYn9DkZen96dKWG3mnkqMRaXULBpI7lrvkafkoLa3x/nxx7Dcfq0\nO7YTNOSWU3Yhh/ILueYQU5MACZAkbAf7YH+/f7OEmNYaIWD33+Hwsgqb6r+bTASETkfKH/9I0e49\nuL/yMi7z5zfJdZuS8vJycnJybvE35OTkYDAYqsZpNJpqzUnOzs6oW1Cxu4YqH5GSksLKlSsZMGAA\nDzzwQNX7xSVxHDs2Hn+/BXTu/NcbDzIazIlfjn7mQod3gc5gYuqru5lQoGby82H4BTvXeq6NiSwA\nDYgwCU7vTuTIlkuUWEistyhjSD9v/jklFDvLmv+IhMFA0Z695K5aRdnZsygcHHCaPRunRx5B7XHn\njEhTmYHy2Fx0ycXY9PVA7dl4jcgbBSHgl5fh+AoY+hKMfK3RL2nS6Uh5/gWK9+3D49VXcZ57x1ST\nNoXJZKKwsPAWJ3ROTg6FhYU3jK3cNbi4uGBhYYEkSVU/wA2v7+az+h4DRvILPqWk5FesrAbj6vIS\nSqVVrc61fft2CgsLWbp06Q2Je2fPPUVe3lHuuzcctfpGfx5Rm83RP3O+hW4T7urf+XB8Nl8ti6Cv\nSc2iD4aiUresmzJZABqBlJg8dn4ZSWmpgV80Wgo9Lfhwdhh9O9xZ/UsjTpO7ejVFe/aAUonD+PE4\nL5iPZbfmaxzdJJhMsP15iPgaRv4Nhv6p8S6l1ZL83HOU7D+A5+t/x+mhhxrtWq0RrVZbFb56c4SS\nXq+nZawDAh+fCwQGnaK42IWoqOHodbULmZ0xYwY9elzrXpdfcIpTp2YRFPQigQHVBAF8OQpKc2Dp\nyTsmflXyxo4LmLan0KObK1Oea5pottpQGwFond6jZsCnqxOzX+vPri+jGB+XT1wWzPnsCM/c35ln\nR3ZCpax5y2rdpzfWfXqjS0oid83X5G/aRMHWrVgPGojLggXYDGn+GuKNgkIBEz80dxT77V+AgIFL\nwKJh4+BN5eUkL1lKyeHDeP7zHzjNmtWg528LaDQavLy8brCLV4cQotqfmj5rjGOKig6Slv5vBt93\nAE/P/2BhEXRX57O2tsbf3/+G73Ip/h0sLFxvrPZZSdJxSD5h9lPVopPcsXMZjDEpCOhefTn11oS8\nA6glJqOJY9sSiNiZiNZWyRqphI6BDnw4uzf+Lne3sBkLCshbv568teswZGZi0akjzvPm4TB5covs\nP1tvjAbY+AREbwG1jTnaInQ6dBoF6vrV2DGVlZH0zDOUHj2G17//jeOMllODXqbuNET5iOzsfZw9\nt5CuXf6Br2815sAf5sLlA+aOXxZ3Z2JNzitl6T8PMLrMgkf+MRBHj5aX1FebHUALCSBvPSiUCgZN\n68T4p3tgZ5R4SmuNLrGE8csOsiki+a620koHB1yffJJOe3bj/fZ/kdQWpP/t78SPvJ+sTz7BkJvb\nBN+kCVGqzMlhj22DnrMgIRx+eATe6QSbFpnb7hl0dzzNzZhKSkh6ajGlx47j/dab8uLfhrCzC+We\nfpuwtg7i3LmnSEz8qlZmKnPC2btYWfnj7T371gG5l+Hidui34K4Xf4DwmCwC9EqsHC1wcG+BYdi1\nRN4B1IOCrDJ2rowkK7GIRHcl67XFTArz5l9Tu+NgdfdRFkIISo8dI3fVaor370fSaHCYMgXn+fPQ\nBLWMCoMNilFvvvOK2gQXfoLyArB0gG4TzTuDoGFQQxG5qlMUl5D01FOUnTmD93//i8PEu3PgybQu\n6lo+Ii19C9HRfyQ09EM8PSbdOuCXV+DEl/DCebC/+8ZGT646QejxIsIGezP8kZbpw5OdwE2IQW/k\n4Po4og+mItw0rNAXYO9oyQezw+gfWPvwMO2lS+SuXkPB1q0InQ7bYcNwnD0L2yFDWnWf2hox6Mw7\ngqhNcPFn0BaClTMET4LQaRAwpKqsRCXGoiKSnlxE2fnz+Lz3LvbjxjXP3GWahNqWjzCZtBw5Oga1\nyoF77tlya0hpWT58EGq+4Zi+ovqTVIPWYGT8q3uYXqDmgcU9CApzq+tXalRkAWgGLh5NY/83MUgW\nCnY5GIgoK2PJiE48d39n1LdxENeEISeHvO++J+/77zFmZ6N0dsZh0iQcpk/DsmvtGna3GvTlcGmv\nOTQv5hfQFYONm7m+UPfp4D8IY3EJiQufpDw6Gp/338N+zJjmnrVME3G35SOSklYTG/cvwnqtxsVl\nyK0Dfl8Gu/8GTx0Ar+oz9qvjYFwWX3wcwUC9miffG4qFVcuMoZEFoJnISSnmlxXnKcwuIyfImq+y\ncujl78hHs8MIcK1bHL/Q6yk+dIiCzVso2rcP9Ho0IcE4Tp2G/aSJqJyc7nyS1oi+DOJ2VYjBr2Ao\nw6jyJDHcifL0Ynw//BC7UaOae5YyTcydykcYDMUcPjICW9uu9A5be2t0nVEPH4WBcyDM316ra/9r\nezSGX1LpGeDEjJdu3yqyOZGdwM2Ei48ts/5yD0FhbjjHl/J3JzdSMooZv+wg608m1SnWWlKrsRsx\nAt9lH9H5wH48XnsNSVKQ8cYbxA0dRvKzz1L022+I65qXtAnUVhAyBR5cDX++hGHMcq7usUGbmo/f\nvZnYnXvOXMAr+aQ56UymXeDkNIB7+m1ArXbk9Om5pKVtuuHzxMSv0Otz6dTxz9WHVkdvhcJkc4Z6\nLTkclYG7UUGHNhD+WYm8A2gEhBCc+y2ZwxvjsXS04JAb7M3IZ0IPL96Y1gOHBmjRWB4TS8GWLRT8\n9NONJqJpU9tcgpkhJ4fEBY+ju3oV3w/extY1HyI3QfweMOnB0d/sLwidbt7St8WcCpkb0OsLOB+5\nhLy8I1XlI/T6XA4fGYmL81B69Pj41oOEgJUjQFsES07UqlBhYk4pi/9zgAmlFsz66z24+Tdyt716\nIJuAWgjpCQXsXBlJWZEeY29HPohPxc1ew/uzwhjUsWHuIqpMRFu2UlyxE9AEB+M4bSr2Eyeicm5Z\ndUpqiyE7m6vz56NPTsHvs0+xGXRd5cWyfLPjOGozJOwDkwGcg66JgUeoLAZtGJNJT0zM30lNW4+7\n2wOo1PakpW1g4ICdWFsH3nrA1SOwahxMeB/ueaJW1/r6yBWOfRtLmIUlC98Z0iJ6gNeELAAtiLIi\nHbv/F0XShTzcezizoiSPS3mlPDW0Iy+O7oJFA9byN+TlUbhjBwWbt1AeGQkqFbbDh+E4bRq2Q4e2\nuigifWYmifMXoE9Px++zz7AZ0L/mwaW55pDSqE3mEFNhAtcu18TAvW3timTMCCFITPqK+Pi3AIG3\n9xyCu/2n+sHfPwJXD8Mfomqdjf74quN0P1FMj3s8GL0gtP4Tb0RkAWhhmEyCkz9f5sSOKzh6WnMh\nUMO66FR6+Djw4ZwwOrrZNvg1y2NjKdiylYJt264zEU3EYdq0VmEi0qenkzhvPoasLPy+WIF1v7v6\nfTZTnAUXtpl3BlcOAQLcQ8xCEDoNXDs12rxlmoesrN0kJ68jJORtNBqPWwfkXILlfc31qGpZmLBc\nb2T033YzJ9+CUQtC6DrAs4Fm3TjIAtBCSYzKYff/ojEaTTgP9+Tf566i1Zv4+6QQ5tzj1yj1gITB\nUBVF1FpMRPrUVK7Om48xNxe/lSux7tO77icrSjc7/qI2Q+IR83uePa6JgXM1pgKZtseOl+DUangh\nEuyqEYjbsD82i88+jWBIuZoFbw/G2r4Z+m7XAlkAWjBFueXsXBlJxuVCOg32Ym1pPocSchkb6sFb\n03viZNN4v1w1moimTjWbiCya/xdbl5xC4rx5GAsL8f/qS6x6NmCz7YIUcz2iyE2QUvF75d2nwkw0\nzVwTXqbtUZZn7vgVOg2mflrrw/9vWxS6XWn09LJnzqu3MUO2EGQBaOEYDSYOb4zn3L5kPALtye1l\nzzsH43G2seC9B8MY3Nm10eegjYsjf8sWs4koKxulkxP2kybiOG0alsHBjX796tAlJnJ1/nxMJaX4\nf/UVVt0b0daad/WaGKSdMb/n29+ccBYyBexbTpNvmXpy6APY83+w+Hfw7F7rw0f/dx9TLgv6juvA\noKkdG35+DYwsAK2EuJMZ7Ft7EaVaQecpAfzj+CUuZZXw5JBA/jS2KxpV4zeaEAYDJb//Tv7mLRTv\n3Ws2EXXrds1E5NI0Mc+6K1e4On8Borwc//99hWVISJNcF4DcBLOJKHIzZJwHJPAfdE0MbO/cwEem\nhWLQwUc9wa0rPLa11odfzi5h0RsHmFqqYdofe+PdueUnXsoC0IrISy/h1y8iyU0rofe4DuwwlbDu\nWBIhXvYseyiMTu5NF29szM+noNJEdP682UQ0bBiO0xrXRKRNuEzivHkIgwH/1auat9RFdpx5VxC1\nCbIugqSADveZxSB4Cti0nSSgdsG59bDpSXhkA3QeXevDV/1+mSM/xNFX0rDw/SEo61DWpamRBaCV\nodcaCf/2IrHHMvAPcUZ9nxt/3RFNidbAaxOCeai//20bzjQGTWUi0sbHc3X+AhCCDqtXoencghps\nZ164JgY58SApzZVKQ6eB7z2gtACVJag0Fc8rHuXcg5aBEPDFMHONqWeO1irxq5J5Xx0j9HQJ3UNd\nGf90A/qjGhFZAFohQgiiD6Vy4IdYrO0s6P9wF944nsDBuGzc7TRM7e3DjD6+dPVs2gzExjQRlcfG\nkjh/ASgVdFi9Gk3HFmpfFQIyIq+JQd6V249XasxioNJUPLe46b2bhcPyujEVr294bnEXx910vcrj\n2rMYXT4IaybCpI+g7/xaH16mMzLs77uZl2/BsIe70n2oT8PPsRGQBaAVk3m1kF+/iKQkX8u90zuR\n6q5iY0QK4TGZGEyC7j72zOjjy+Re3rjYNm33MGN+PoW//EL+5i2UnztnNhENHYrDtKnYDRtWKxNR\n+cWLJM5fgKTR4L96FZrAVhKOKYTZaZx7GYw6c7tLgxaM2pue66p5r/L5zcfpwFB+43Ma6O9SWZP4\nVLyvtgTnjuAdBl5h4B5sHtcW+HaOueXjHyLNtaVqyb6LmSxfEcH9ZRbM/fcg7F1bRwOYJhMASZKc\ngR+AAOAKMEsIkVfNOEfgS6A75t/sx4UQR+50/vYoAADlJXr2ro7myvkcOvVzZ+RjwRToDGw7k8rG\niGSiUgtRKSSGd3VnZl8fRnbzaNCM4rtBGx9vrkW0dRuGrCyUjo7YT5qE47SpaIKDb5vTUBYVRdLj\nTyBZW9NhzWosruvjKoNZZEyG68SivAbhuP7z6gSnUlhuc5yuFLJjzE15ABRq8Agx11TyqhAFj9B6\nt+5scrLj4eO+MOwVGPGXOp3i71sjKdubTi9HGx7956A7H9BCaEoBeBvIFUK8JUnSK4CTEOLlog5Z\nHQAAIABJREFUasatAQ4KIb6UJMkCsBZC5N/p/O1VAACESRCx6ypHtybgH+zM+Kd7olSbF/mL6YVs\nikhh8+kUsoq0OFqrmdzLmxl9fOnp69CkDeaFwUDJ4cPkb95M8Z4KE1HXrjhMm4rDpEm3mIjKzp8n\n8YmFKG1t8f96DRa+vk02V5kaEMJs1ko7A2lnIfWM+XlZxb2cQgVuwWZR8A4zP3p0r3U5hSZl+4tw\nep357r8OUVxCCEb8dx8zEqHXMF+Gzu7SCJNsHJpSAGKA4UKINEmSvIBwIUTXm8Y4AGeAIFHLi7Vn\nAagk+vdU9q29SFBvN8YuDEVxnTPYYDRxMD6bjaeS2RWdgc5gopO7LdP7+DCttw9eDk27Zb2Tiag8\nOprEhU+idHKiw+pVqH1ah021XSIEFCRdE4NKYSjNNn8uKcCt23U7hV7mDGtNw5c1qTWluebErx4z\nYUo1VUHvgktZxTz+1kFmlWiYsKQnAT0aPzenoWhKAcgXQjhWPJeAvMrX140JA74AooFewCngeSFE\nSQ3nXAQsAvD39+979erVOs+vrXB2bxKHfoyj6wBP7p8XXG0lwoIyPTvOp7HxVDInr+YhSTC4kysz\n+vgyNtQTK4vGzym4nupMREKnQ+nmSofVq1F73X0fVpkWghBQmGoWhNQKUUg7A8UZFQMkcwG+qp1C\nmFkULO2bdp4H3oXf/mWO/HGvW8TaV4cuc/DHWAYYLFj4/lDUmqb9+6kPDSoAkiTtAaqrfvQqsOb6\nBV+SpDwhxA2ZEpIk9QOOAvcJIY5JkvQRUCiE+NudJifvAK5x4ufLHP/pMt2H+TB0TpfbmnmuZJew\nKSKZjREppOSXYWOhZHwPL2b09aV/gDOKJixlKwwGSo4cIX/TJgxZWfi89x5qj9rVYpFp4RSmXROD\nyp1CUeq1z1063bhT8OoFVo41n68+GLTwYQ+ziWrupjuPr4G5Xx0j5GwJIUFOTHmhHrWomoHaCMAd\nm1oKIWrsuydJUoYkSV7XmYAyqxmWDCQLIY5VvN4AvHI3k5O5Rr/xAejLjZzenYiFpZKBUzvWKAIB\nrja8OKYrL4zqwvEruWw8lcyO82n8eCoZXycrpvfxZUYfHzq41K1NZW2QVCpshwzBdkg1vVll2gb2\nXuafruOuvVeceaM/Iek4RG689rlT4I0+Ba8wsG6AwoSRm8w7kqmf1fkUpToDUXG5DNRp8A9p24l/\n9e1qvA2YB7xV8XhLrrUQIl2SpCRJkroKIWKA+zGbg2RqgSRJDJreEZ3WSMTORNQaFf3GB9z2GIVC\nYmCQCwODXPjHlFB2RqWz8VQKy3+LY9neOO4JcGJ6H18m9PTC3rJ19QqQaeHYupszb6/Pvi3JvrZT\nSD0DqafN9ZgqcfS/MfrIOwxsamF7FwKOfGJ2WHccWeepH47PwUdrvrnyD2151XIbkvr6AFyA9YA/\ncBVzGGiuJEnewJdCiPEV48Iwh4FaAAnAgurCRW9GNgHdijAJ9qyJJvZYBoNndabXyNpXsEwrKGPz\n6RQ2nkrmUlYJGpWCMaGezOjjw5DObihbcLcjmTZGaW6FKFxnQspNuPa5ve+tO4WayjknhMPXU2Dy\nx9Bnbp2n9Orm85SGp9PT0or5b93XpFF1DYGcCNbGMRlN7FwZRcKZLEbM7UbIfXWrXCmE4GxyAZsi\nktl2NpX8Uj3udhqm9fZhejNkHcvIAOZWn+nnrjMhnTWX4qhMjrPzutGn4B1mfu/bWebxf4isczKb\nEIIhb+3jwWToPsCL+x9rnsq49aFBfQAyLQ+FUsGYJ0L5+bNzhK+7iFqjpHO/2jtWJUkizM+RMD9H\nXp0QzL6LmWw4lcJXhy6z4kBCs2Ydy7RjrBwhcKj5p5LyQkg/f6MJKXYnVaJg4w4lmTDi1XplMsdn\nFmPK0aIyavAPadvmH5B3AK0avc7IT8vOkJFQyANP92iwWOXsYi0/nTVnHUemNH/WsYxMtWiLzTWa\nKncKJZkwfWW9nMkrDyQQvjGOe3Vqnnh3CJY2rc83JpuA2hHaMgNbPzhNbmoJE5/thW/Xhq1XHpNe\nxMaI5BaRdSwj09g8vPIowVGlBHvZM/PlWvShbkHIAtDOKCvWsfm90xTlljPl+TA8gxwa/BqVWceb\nIlLYFZWOtiLreEYfX6b19sHToZXVipGRuYlirYFB/7eLp/Is6T8hgP6Tgpp7SnWiNgIg7+XbAFa2\nFkx5IQxrewu2f3yW7OSiBr+GSqlgRFd3lj/Um+OvjuLN6T1wtFLz318vMuitvcz96hhbTqdQpjM2\n+LVlZJqC3+Oz8dYqkAD/0LYd/1+JvANoQxRml7H5vQiMBhPT/tgHJ8/GT/S6mlPCxogUNkUkk5xX\nhq1Gxfgenszo48s9TZx1LCNTH/6y6TxFBzIIU1jw+DuDb6i71ZqQTUDtmLz0Eja/F4FSpWDaH/s0\nWQ1zk0nckHVcojPi52zFtN5Nl3UsI1NXhBDc++ZvzE5X0K27G+MW1b55fEtBNgG1Y5w8bZj8fBh6\nrZGtH56mJF/bJNetzDp+58FenHhtFB/ODiPAxYblv8Ux7J1wHvz8MD+eTMJgNDXJfGRkakNsRjH6\nPC1qnWjz2b/XIwtAG8TV146Jz/aitEjP1o/OUFasa9LrW1uomNrbh7VPDODwKyN5eVw38kr1vLTh\nHBOXH+JwfHaTzkdG5k7si8kkUG+u+Nke4v8rkQWgjeIZ6MCEZ3pSmF3GT8vOoi0zNMs8vByseHp4\nR3b/YSifPdKHYq2Bh788xlNrT5KYU9osc5KRuZl9FzMJVVjg7G2DrVP7iWiTBaAN49vViXGLupOT\nXMzPH59Fr22+CB1Jknighxd7XhzGS2O7cjAum1Hv7+ftXy9SrG0ecZKRASgs13P2Sh6u5aJd3f2D\nLABtnoAerox+IpT0hAJ++fwcRn3z2uAt1UqWjOjEvj8NZ2IvLz4Nv8SId8PZcCoZk6nlBiTItF1+\nj8vGWychmWjz5Z9vRhaAdkCnvu6MmNuNpAt57PwyElMLcMR62Fvy/qwwNj9zLz6OVvzpx7NM+/R3\nTl29Y5FYGZkGJTwmiy5ChUqtwKtzwydRtmRkAWgnBN/rzZDZnbl8Npu9X19AtJC77d7+Tmx6+l4+\nmN2L9MJyZnx2mOe/P01aQVlzT02mHSCEIDw2ky5CjXcXJ1Tq1tP6sSGQq4G2I3qO8ENXbuTY1gTU\nGhXDHrp9a8mmQqGQmNbblzEhnny+/xIrDiSwKyqDxcM6smhoUJP3M5ZpP1xIK6I8T4emTNGuwj8r\nkXcA7Yy+4zrQZ6w/UQdSOLzpEi0pEdBGo+KPY7qy98VhjOzmzgd7Yhn1/n5+OpvaouYp03bYF5NJ\ngMG8DLY3BzDIAtDukCSJgVM70mOYD2d2J3Jyx5XmntIt+Dlb88kjffh+0UAcrNQ8+91pZq04QmRK\nQXNPTaaNsT8mi14qDXbOljh6WDf3dJocWQDaIZIkMWR2F7oO9OT4T5c5uzepuadULQODXPjp2cG8\nOb0HCVklTPr4EC9vOEdWUdNkN8u0bQrK9Jy+mod7mbn3b0swhzY1sg+gnSIpJEbO7YZBa+TQj3Go\nNUpCBtettWRjolRIPNTfnwk9vVi+N47Vh6/w8/k0nh3Zifn3BaBRyf4BmbpxKC4bD72EZBDtLvyz\nEnkH0I5RKBWMfiIU/1Bn9n1zkbgTGc09pRqxt1Tz6oQQdr4wlAGBzrz5y0XGfnCAPdEZsn9Apk7s\ni8mkG2oUCgmfbg3bSKm1IAtAO0epUjDuqR54d3Jkz6poLp9r2XV6gtxs+Wr+Pax5vD8qpYKFX5/k\nsf8dJzaj4XsgyLRdTCZBeEwWwajxCLJHY9U+jSGyAMigtlAy4ZmeuPrZsvOLSJIu5jb3lO7IsC5u\n/PL8EF6fFMLZpHwe+Oggr2+NJL+0aQvfybROotMKKS3UYllsbDfNX6pDFgAZACysVEx6NgwHdyt2\nfHae9ISWH3GjVipYcF8g+18awSMD/Fl79CrD3glnzeErctlpmduy72ImAYb2V/3zZmQBkKnC0lbN\n5OfDsLG34KflZ8lKbB1mFScbC/45pTs7nh9Cdx97Xt8WxfhlBzkYl9XcU5NpoYTHZtFbbYmVnRo3\nP7vmnk6zIQuAzA3YOGiY/EIYFpZKti07Q25aSXNP6a7p5mnPuicG8MXcvpTrTcz96jgL15zkSnbr\n+Q4yjU9+qY7TV/PwKge/YGekdty2VBYAmVuwd7Fiygu9kRQS2z46Q2F266nLI0kSY0I92f3iUF55\noBtHLmUz+oP9vLnjAkXl+uaenkwL4EBcNm4GCUlratfmH5AFQKYGHD2smfJ8GAadubVkcV7rSr7S\nqJQsHtaRfS8NZ2qYD18cTGDEu+H8cCIRYwsphCfTPIRfzCRYUgPg107j/yuplwBIkuQsSdJuSZLi\nKh6rDaaVJOkPkiRFSZIUKUnSd5IktZ+WO60YFx9bJj0bRlmRnm0fnaasqPVF2LjbWfLOg73YuuQ+\nAlxseHnjeaZ8cojjl1t+pJNMw2MyCfbHZtFdocHVzxZre4vmnlKzUt8dwCvAXiFEZ2BvxesbkCTJ\nB3gO6CeE6A4ogTn1vK5ME+ERaM+EJT0pzCln27IzaEtbpxmlp68jPy4exLKHepNTrGPWiiMs/TaC\nlPzWY96SqT/nUwooKtZhVWRo1+GfldRXAKYAayqerwGm1jBOBVhJkqQCrIHUel5Xpgnx6eLEA4t7\nkJtawvaPzzVra8n6IEkSk3t589sfh/PCqM7suZDByHfDeX93LKU6uS1le2BfTCYdDAowte/wz0rq\nKwAeQoi0iufpgMfNA4QQKcC7QCKQBhQIIXbVdEJJkhZJknRSkqSTWVlyGF9LoUOoC2OeCCXjcgE7\nPjuHQd86RQDAykLJC6O68NsfhzM21JNle+MY+e5+tp5JkctKtHHCY7Lop7FCrVHiGdS+un9Vxx0F\nQJKkPRW2+5t/plw/Tpj/cm7566nwC0wBAgFvwEaSpEdrup4Q4gshRD8hRD83N7dafyGZxqNjH3dG\nPhZM8sU8dq6MwtjKk628Ha1Y9lBvflw8CDc7Dc9/f4aZnx/hbFJ+c09NphHIKdZyNikfn3IJ325O\nKFVyDMwd/wWEEKOEEN2r+dkKZEiS5AVQ8ZhZzSlGAZeFEFlCCD2wCbi3Ib+ETNPRbZAXQ+d04cq5\nbPauvtAmGrnfE+DM1iX38fbMnlzNKWXKJ7/zpx/PkllY3txTk2lADsZl42iUkEqNsvmngvpK4DZg\nXsXzecDWasYkAgMlSbKWzAW37wcu1PO6Ms1Ij+G+DJwaRNyJDPZ/G9MmzCYKhcSsfn7s+9MwFg/r\nyLYzqYx4N5xPw+Mpb8XmLplr7IvJpLvCHPXT3sM/K6mvALwFjJYkKQ7znf5bAJIkeUuStANACHEM\n2ABEAOcrrvlFPa8r08z0HRdA33EdiD6Uyu8b49uECADYWap55YFu7H5xKPd1cuXtX2MY/cF+fo1M\nbzPfsT1iNAkOxGbRQ6XBwd0KBzer5p5Si6BeNVCFEDmY7+hvfj8VGH/d69eB1+tzLZmWx4ApQei0\nRs7uScJCo6T/pKDmnlKD0cHFhi8e68fv8dn886doFq87xaAgF/4+KYRgL/vmnp5MLTmbnE9hiR7b\nEjX+Q26JVWm3yF4QmTojSRJDHuxMt0GenPj5Cqd3Jzb3lBqc+zq58vNzg/nXlFAupBcyYdlBXt18\nntyS1pcU154Jj8nCz6hAGIRs/78OWQBk6oWkkBgxN5iOfdw5vDGeqIMpzT2lBkelVDB3UADhfxrO\nY4MC+P5EEmM/PCBnE7ciwmMyGWBljUIl4dOlfXb/qg5ZAGTqjUIhMfrxEDp0dyH82xhijqU395Qa\nBUdrC/5vcig/LR2MrUbFQyuP8sWBS7JvoIWTVaTlXHIBfjoF3p0cUWvkPtKVyAIg0yAoVQrGLeqO\nT2dH9q65QMKZtpvEF+Jtz7al9zEmxIM3dlxk8bpTFMqVRlssB2KzsDWBVKDHTzb/3IAsADINhspC\nyfhneuLewY6dX0aSFN12TSR2lmo+faQPr00IZu+FTCYvP0R0amFzT0umGvbFZNJDqQHMGe0y15AF\nQKZBsbBUMXFpL5w8bNjx+TlS49tuVq0kSSwcEsT3iwZSpjcy7dPf+fFkUnNPS+Y6DEYTB+Oy6a22\nxMbBAmdvm+aeUotCFgCZBsfSxtxa0tbJkp8/bj2tJetKvwBntj87hD7+Try04RyvbDwnJ4+1EM4k\n5VNYqseuwIBfiDPmXFSZSmQBkGkUrO0tmPx8GBprNds+OkNuattuy+hmp2HtE/15ZnhHvj+RxIzP\nDpOYU9rc02r3hMdk4SMUmLQmufxzNcgCINNo2DlbMvmFMBRKia0fnaYgq20viCqlgj+P68aXj/Uj\nKbeUicsPsic6o7mn1a7ZF5PJICsbkMCvm+wAvhmpJYew9evXT5w8ebK5pyFTT3JSitn8fgQGnQmN\ntQqVWoFSpUBZ8XjD6+ueq1S3vq+6fszNx1Yep1agUEmo1MqK9yWUKkWTbv8Tc0p55ttTRKYU8szw\njrw4ugsqpXy/1ZRkFpbT/429vKR0wMPekpkv92vuKTUJkiSdEkLc1ZetVykIGZm7wcXHlmkv9iH6\n91QMOhNGvQmD3oTRUPGjN6EtM2AoND+vfK/y0WAwVVNovPaYRUO6VVDuVoyue+3dyRE3f7sar+Xv\nYs2Gxffyj5+i+DT8EqcT81n2UG/c7DT1/yIyd0V4bBaWJqBAh99A7+aeTotEFgCZJsHFx5Yhs7rU\n6VghBCajuCYINYjEDa/1JkyGW8eaXwuMemPFe6LiPSMGnQltqeHGY657fn3pa0khMWByIH3GdEBS\nVL+zsFQreXN6T/p2cObVzeeZsOwgnzzSh3sCZFNEU7A/Joueag0IOfyzJmQBkGnxSJJUZcbBsvnm\nYTKZRUhXauDQj3Ec3ZJASmw+o+aH3La5+My+voR62/P0ulPM+eIof3mgG08MDpQjUhoRg9HEgbgs\nHtXYorE24t6h5t1ae0Y2SsrI3CUKhYTaQomNo4YxC0MZ/khXUuPy+eHfx0m6ePukt2Ave7Y9O5hR\nwe78++cLPPNNBEVy9nCjEZGYT1GZAYcCI77dnFDI/pdqkf9VZGTqgCRJhA7x4cFX+qGxVrHtozMc\n25aA6TZtMu0t1Xz+aF9eHR/MrugMJn/8OxfT5ezhxmBfTCYeQoGxxCCHf94GWQBkZOqBi48tD/7l\nHroN9OTkjits/fAMxXnaGsdLksSTQ4P4duEAirUGpn7yO5sikptwxu2DfRczGWxnzvqVyz/XjCwA\nMjL1RK1Rcv+8EEbNDyYzsYgf/n2cK+ezb3vMgCAXfn5uML18HXlx/Vn+uvm8nD3cQKQXlHMxvYiO\nBhXO3jbYOjWj46iFIwuAjEwD0XWgF7P+0g8bRw0/f3KO3zfGYzTUbBJyt7Pkm4UDWDysI98eS+TB\nz4+QlNu2k+WagvCYTNQCyNbK1T/vgCwAMjINiJOnDTNf6Uv3YT6c2Z3IpncjKMwuq3G8SqnglQe6\nsfKxflzJKWHi8kPsu5jZhDNue4THZNFLY4kwCjrIzd9viywAMjINjEqtZNhDXRn7ZHfy00v44T8n\nuBRx+0V9dIgH258djI+jFQtWn+DdnTEYTS03S7+lojOYOBSfTT9La1RqBV6dHZp7Si0aWQBkZBqJ\nTn3dmfVqfxzdrfj1i0j2fxeD4TZ2/g4uNmx65l5m9/Pj433xPPa/Y+QU1+xQlrmVU1fzKNYacC40\n4t3FEZVa7v51O2QBkJFpRBzcrJj+Ul/CRvkRuT+FDf89RX5GzXZ+S7WS/87sydszenLySh4Tlh3i\n1NW221inoQmPycQFBfp8Hf6y+eeOyAIgI9PIKFUK7pvZmQnP9KQ4r5wf3jhxx77Js+7xY9Mz92Kh\nUjB7xVH+d+iy3Hv4LgiPyWKYvS0A/qGyA/hOyAIgI9NEBPR0Zc5r/XHzs2XPqmj2fn0BvbZmk1Co\ntwM/PTuYEd3c+ef2aJZ+d5piraEJZ9y6SM0vIyajiM4mNXbOljh6WDf3lFo8sgDIyDQhtk6WTP1D\nb/qND+DikTR+fPMEOSnFNY53sFLzxdy+vPJAN345n8bkjw8Rm9G2O6zVlfCYLBQCpKxy/ELl7l93\ngywAMjJNjEKpYMDkICY/F0Z5qYEf3zpJ1MGUGk08kiSZcwWeHEhhmYEpH//OltMpTTzrls++mEx6\nWVlh1Jrk8M+7RBYAGZlmwi/YmTmv9cerowPh38Sw+6sodGU1m3gGBrmw47nB9PBx4IUfzvDalvNo\nDXL2MIDWYOT3+GwGWlsjKSR8ujk195RaBfUSAEmSHpQkKUqSJJMkSTV2oJEkaZwkSTGSJMVLkvRK\nfa4pI9OWsLa3YPJzYQyYEkR8RBY/vHGCzKs1F4hzt7fk2ycH8NTQINYdTWTW50dIzmuf2cN6o4mI\nxDw+2RfPY18dp1RnxKXYhGeQPRorudL93VCvlpCSJAUDJmAF8CchxC39GyVJUgKxwGggGTgBPCSE\niL7T+eWWkDLtidT4fHZ/FUVpoY57Z3Si5wjf29qxf41M56Ufz6JUSnw4O4zhXd2bcLZNj8FoIjK1\nkCOXcjiakMPJK7mU6Mw7oK4edozq6IL1jgwGTA6i3/iA5p1sM9JkLSGFEBcqLni7Yf2BeCFEQsXY\n74EpwB0FQEamPeHdyZHZr/Zn75poDq2PIyUmj5GPBWNpo652/LjunnT1tOPpdadYsPoEz47szPP3\nd0ZZQ4ey1obRJIhKLaha8E9cyauKgursbsuMvr4MDHJhQKAzLrYaYo6ls4cMOfyzFjTFPskHSLru\ndTIwoKbBkiQtAhYB+Pv7N+7MZGRaGJa2asY/05NzvyVzeFM8P/z7OGMWdserY/UlDQJdbdj8zH38\nbWsky/bGcToxj4/m9MbZpuYOZS0Vo0lwIe3aHf7xy7kUVSz4Hd1smNrbu2LBd6m2t3JidA6Wtmrc\n/OTuX3fLHQVAkqQ9gGc1H70qhNja0BMSQnwBfAFmE1BDn19GpqUjSRK97vfDq5MDO1dGsvm9iNv2\nH7ayUPLOzJ706+DE37dFVfUe7uPfsh2hJpPgQnohRxNyOXIph+OXcygsNy/4Qa42TOzlzaCOLgwM\ncsbd7vYlnYVJkBSdi1+wc409mmVu5Y4CIIQYVc9rpAB+1732rXhPRkbmNrh3sGfWq/0JX3fxjv2H\nJUliTn9/uvs48PQ3p5i94givjg9m3r0BLSYe3mQSxGYWceRSDkcu5XDsci4FZea2mAEu1ozv4cWg\njuY7fE+Hu6/hX5hdRuzxdMqK9HSQzT+1oilMQCeAzpIkBWJe+OcADzfBdWVkWj0aKxVjFobi09WJ\nQ+vj+OHfxxn9eAi+3apf6Lr7OLB96RD++OMZ/u+naE4l5vPW9B7YaJo+KkYIQVxmcZVJ59jlXHJL\ndAD4OVsxNtSDgUEuDAxywdvRqlbnzUkpJuFMNpfPZpGdZE6kcw+wJ6Cna6N8l7ZKfaOApgHLATcg\nHzgjhBgrSZI38KUQYnzFuPHAh4AS+J8Q4j93c345CkhG5hrZycXs+jKSvIxS+j0QwD0TAmpsdm4y\nCT4/cIl3d8YQ5GbL54/2oZN749rGhRBcyqpc8HM5mpBDTsWC7+NoVWHOMZt0fJ1qV6bBZDSRdqmA\ny2eySTibRVFOOUjg1dGBwF5uBPZyxdFdLv0AtYsCqpcANDayAMjI3Iiu3MDB72O5eDQd786OjH48\nFFunWx2ilRy+lM1z352mVGfkrRk9mdzLu8HmIoQgIbuEowk5VYt+dkX5ai8HSwYFuTCwowuDglzw\nc6794qzXGUmKzuXy2SyunMuhvESPUqXAN9iJoF5uBPR0rdYc1t6RBUBGpo1z8Wga+7+LRaVWcP+8\nYAJ61Gz6yCgsZ8k3EZy8mse8QR14dUIIFqra54AKIbiSU3rdgp9DZpF5wfew1zAoyKXqLt/f2bpO\nvofyYj1XzmeTcCaLpOhcDHoTFlYqAnq4ENjLDf9QZyws5SSv2yELgIxMOyAvvYSdK6PISSkmbLQ/\nA6cGoazBJKQ3mvjvLxf58tBlwvwc+fSRPne0uwshSMot40hCdlWkTnphOQBuduYFf2DFoh/gUrcF\nH8xO3Mtnzfb81Lh8hABbJw2BPV0JDHPDu4tjjd9L5lZkAZCRaScYdEYObYgn6kAKHoH2jHkiFHvX\nmhf2X86n8dKGc6iVEh/N6c3QLm43fJ6UW8qRBPPd/dFLOaQWmBd8V1sLBgS5VN3lB7na1HnBr8mJ\n6+xtQ1CY2Z7v5m/XYqKXWhuyAMjItDPiT2Wyb+0FkCRGPtaNjr1rLguRkFXM0+siiM0s4tmRneng\nbF216CfnmRvYO9tYMDDIueouv5O7bb0WZNmJ23TIAiAj0w4pyCpj15eRZF4toscwH+6d2anGnril\nOgOvbY5kU0VZaUdrNQMDr9nwO7vboqhnQpXsxG0eZAGQkWmnGA0mjmy5xNk9Sbj62TJ2YfcaO2MJ\nIThxJQ87SxVdPezqveBD9U5cjbWKDj1cCOwpO3GbAlkAZGTaOZfPZbN3TTRGg2D4w13pOqC6ai4N\nQ41O3F5uBIa54t1ZduI2JbIAyMjIUJRbzu7/RZEWX0C3e70YOrsLak31JqHaIDtxWzZNVg5aRkam\n5WLnbO4//P/t3XuMVGcZx/Hvj5vIQsG2qNxakBIuEqWm2WgXG1KV1lqvbbS29Q+vMdqbJDXWNFH/\nskmNl0QlKrsEU7RpgKaICrRarRCVdSmWsnRtXVlZ1FJTQVYCRHj847zodlu3MLvTd+ec3yfZ7Dmz\nZ8953kxmnnkv85wdm/5Ex+Yenu4+zBUfX8x5Myae9bkGm8S99JqLPInboNwDMKuA/Z3P8uDqPZw4\ndpI3v38ei5ZOf9FP6J7EbUzuAZjZc8xadC4fuLOZh1Z38ou1XRzo+gfLbljAuAG3TvRSDdAGAAAG\nVklEQVQkbrX4mTSriKbJL+Odtyxh5+Yedvyom6d7jnDFx17L+KaxLziJu7BluidxS85DQGYV9Jcn\nD7G1dQ9HDx/n9FuAJ3HLwUNAZjao6fOmcN2dzXRs6WHCpHHMWeJJ3CpyAjCrqPETx9JyzUW5w7CM\nPLBnZlZRTgBmZhXlBGBmVlFOAGZmFeUEYGZWUU4AZmYV5QRgZlZRTgBmZhU1oktBSHoG6Knx388H\n/j6M4eRUlraUpR3gtoxEZWkHDK0tF0bE1DM5cEQngKGQ9LszrYcx0pWlLWVpB7gtI1FZ2gEvXVs8\nBGRmVlFOAGZmFVXmBPDd3AEMo7K0pSztALdlJCpLO+Alaktp5wDMzGxwZe4BmJnZIJwAzMwqqnQJ\nQNKVkrokPSXpc7njqZWkNkkHJT2eO5ahkjRL0sOSOiXtkXRr7phqJWm8pB2Sfp/a8qXcMQ2FpNGS\nHpW0KXcsQyFpn6TdknZJauj7yEqaImmdpCck7ZX0prpdq0xzAJJGA38A3gb0Au3AByOiM2tgNZB0\nGdAHfD8iFueOZygkTQOmRcROSZOADuA9Dfq8CGiKiD5JY4FtwK0R8ZvModVE0grgEuCciLg6dzy1\nkrQPuCQiGv6LYJLWAL+KiFWSxgETIuJQPa5Vth5AM/BURHRHxAngXuDdmWOqSUQ8AjybO47hEBF/\njYidafsIsBeYkTeq2kShL+2OTT8N+SlK0kzgHcCq3LFYQdJk4DKgFSAiTtTrzR/KlwBmAPv77ffS\noG80ZSVpNnAx8Nu8kdQuDZvsAg4CD0ZEo7bl68BngVO5AxkGATwkqUPSJ3IHMwRzgGeA1WlobpWk\npnpdrGwJwEYwSROB9cBtEfHP3PHUKiJORsQSYCbQLKnhhugkXQ0cjIiO3LEMk6XpOXk78Ok0hNqI\nxgBvAFZGxMXAv4C6zWWWLQEcAGb125+ZHrPM0nj5emBtRGzIHc9wSF3zh4Erc8dSgxbgXWns/F7g\nckn35A2pdhFxIP0+CNxPMRzciHqB3n69ynUUCaEuypYA2oF5kuakyZPrgI2ZY6q8NHHaCuyNiK/m\njmcoJE2VNCVtv5xiwcETeaM6exFxR0TMjIjZFK+Tn0fEjZnDqomkprS4gDRcshxoyNVzEfE3YL+k\n+emhtwB1Wywxpl4nziEi/i3pJmALMBpoi4g9mcOqiaQfAsuA8yX1Al+IiNa8UdWsBfgQsDuNnQN8\nPiJ+kjGmWk0D1qQVZ6OA+yKioZdQlsCrgPuLzxmMAX4QEZvzhjQkNwNr04fYbuDD9bpQqZaBmpnZ\nmSvbEJCZmZ0hJwAzs4pyAjAzqygnADOzinICMDOrqFItA7XqknQe8LO0+2rgJMVX6gGORsSlw3y9\nCcD3gNcBAg5RfCFsDHB9RHx7OK9nVg9eBmqlI+mLQF9EfKWO17gDmBoRK9L+fGAfxfcENjV6BVer\nBg8BWelJ6ku/l0n6paQHJHVLukvSDam+/25Jc9NxUyWtl9Seflpe4LTT6FdmJCK6IuI4cBcwN9Wl\nvzud7/Z0nsdO3z9A0uxU731tqvm+LvUqSHF1puPrlsTMPARkVfN6YCFFqe1uYFVENKeb1NwM3AZ8\nA/haRGyTdAHFN8sXDjhPG7BV0rUUQ09rIuJJisJdi1NhMiQtB+ZR1KYRsDEVKvszMB/4aERsl9QG\nfErSauC9wIKIiNNlJ8zqwT0Aq5r2dH+C48Afga3p8d3A7LT9VuCbqWzFRuCcVMn0vyJiF/Aa4G7g\nXKBd0sAkAUVdmuXAo8BOYAFFQgDYHxHb0/Y9wFLgMHAMaJX0PuDo0Jpr9v+5B2BVc7zf9ql++6f4\n3+thFPDGiDg22InSjWE2ABsknQKuoqh42p+AL0fEd57zYHFfhIETcJHqWTVTFAG7FrgJuPzFm2V2\n9twDMHu+rRTDQQBIWjLwAEktkl6RtscBi4Ae4Agwqd+hW4CPnO5BSJoh6ZXpbxf0u9/r9cC2dNzk\nVCjvMxRDVmZ14R6A2fPdAnxL0mMUr5FHgE8OOGYusDKVuh4F/BhYn8btt0t6HPhpRNyehoZ+napV\n9gE3UixT7aK4eUkbRcnflcBk4AFJ4yl6Dyvq3FarMC8DNcsgDQF5uahl5SEgM7OKcg/AzKyi3AMw\nM6soJwAzs4pyAjAzqygnADOzinICMDOrqP8ApLJggqpT27cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0683657940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fPogbB7ZtwlhLmoBUKWLFdFo9P3x8iq9fO4qTqwO3/CmOkTf3UIW/GVXW6Xh4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\n1vLDOr2B704W8sO6RCJ3biY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ngl94HueePSl65RUys7IJe/MNHIOCLB2a0kLna/vGNXm+\nRUpTbb/PiwQFdq7afnNUAlCUVhBC4HfPIpyiu5P32OOcm30rYW++geuAAZYOTbkKl9b2HRw8CA29\nnZCQzlvbb06nWwxOUTpaw5kz5Cx9gKaSEoKf+ydeN9xg6ZCUZhhr+z+Rm7fqotp+aOgdBAXegL19\n52jG69KLwSlKR3Pp2ZOo1V+Q88gj5D32ONq0NAIeflgtHWEljLX9tabafkaXre03RyUARTEDB19f\nIpcvJ//ZZyl9620a0zMIeeF57Nw6dxuytWqutu/1c9t+56ntt5VKAIpiJsLJieC//x3nmBiKXnqZ\nc3OzCX/jDRyDgy0dWpfR2FhGQcG6X9X2Q0PuRKPpZenwrI5KAIpiRkII/BYuxDk6mtw/PMbZW28j\n/I3XcR00yNKhdVp6fR1lZTspLNpEUdGWn2v7ffu8RGBggqrt/4Y2dwILIcKBFRi3hpTAMinlq5cc\nMwHYAJw1PbVWSnnpvsG/ojqBFVumTUsje+kDNBUWEvzPf+B1002WDqnT0GoLKSn5geKSbZSX78Jg\naMTBwZNu3WZ0+dp+R3cCNwGPSSkPCSE8gINCiK1SyuRLjvtRSnmjGa6n2BidQcfhwsMU1RcxIWwC\nGqeusdeuc0wMUV98Tu7vHiXvj39Cm5pGwKO/U53DrSClpKb2NCXF31NSso2q6mMAuLiEERoyB3//\nyXh7D8POztHCkdqWNicAKWU+kG/6uVoIcQoIBS5NAEoXUlpfys7cnSTlJLE7bzc1uhoAXB1cmRo5\nlVtib2FI4JBOv4yCg48PEe+9S8E//knpsmVoM9IJffFF7NzdLR2a1TMYGqmo2E9xibHQb2jIBcDT\nczA9oh/D338y7u49O/3vUHsy6zwAIUQUkAT0l1JWXfD8BGAtkAPkAo9LKU9e5hyLgcUAERERcZmZ\nmWaLT2k/UkpSylJIykkiKSeJ4yXHkUgCXAMYFzaOsWFj8XXxZUPaBjaf3UxdUx1RnlHMip3FTT1u\nwt/V39IfoV1JKSn/+BMKX3gB59hYwt98A8fQ0I4MAAx6MDQZv6T+l8d2DmDvZPpyBAsWqDpdJaWl\nOygu+Z7S0h3o9TXY2Tnj6zsGf//J+PtNxNk50GLx2YKWNAGZLQEIITTADuCfUsq1l7zmCRiklDVC\niATgVSll7JXOqfoArFudro59+fvYkbODH3N/pKiuCIAB/gMYGzaW8WHj6e3bGzth96v3bTm3hXVp\n6zhcdBgH4cD48PHMip3F6JDRONhZ6dgEKaG6AIpOQm2pqRA1FagG/cUFrKEJpOHixwY9Ncn55H60\nH+FgR9j8gbhFeFxyjgu+S/1lzq2/5NpNYDD89rWl4eo/p70T2Dsbk4GD6bu9s/F5B6cLkoVTy17/\n+bULz+1EvaGC4oYTlNQfpqLuFBIDjg7eBHhfg7/vBHx9rsHeycv4XtV8dkUdngCEEI7A18AWKeW/\nr+L4c0C8lLLkt45rbQLIyfkEjUcfvDyHIIT6hTGnnOocYy0/N4n9+ftpNDTi7ujO6JDRjAsbx5jQ\nMS2qzWdUZrAudR0b0zdS1lBGoGsgM2JmMDN2JuEe4e34Sa5AWw1Fp6DwJBQlQ2GyseCvL2/5uYS9\nsZZt+tJW2ZO9zZmmGug23g7vXg4XvY6d3cWPhT3YXXiOSx7/fP7LfBe/9V47Y0LRN4JeC02Npp9N\nX01a0OuMr+l1pscXvt74y3t/ft10fJMW47iQi0mgysOBYj8nSvycqHU3Jnz32ib8SxsJKG3Es7qJ\nZu9D7Bx+lUB+/nJyA98e4N8T/GON3/16GI/rQjo0AQhjA9xHQJmU8tHLHNMNKJRSSiHEcGANECmv\ncPHWJAB9Uy0/7hiCXuhxdg4mKDCBwMAEPD0HqbbCVmgyNHGk6AhJuUkkZSeRXpkOQKRnJOPCxjEu\nbBxxgXE42ret802n17EjZwdrU9eyK28XBmlgeLfhzIqdxZTIKTjbt9Mfsb4JStOMhXthsqmwPwEV\nWb8c46SBwD4Q2BeC+hm/ewSD/ZUKYFMB28zvnb6igpxHf0/d3r343XsPAb//PcLevn0+oyXpm0Df\niL6xkrLy3ZSUbaekcg+NTeUI7PB27YO/2yD8nfvhZudzmQSjvSTZNJecGo1JuzQDKi/4vxN24B0J\nAb1+SQrnv9x8Lffv0o46OgGMAX4EjgPn7zOfBiIApJRvCyEeApZiHDFUD/xBSrn7Sudu1R1AfQVN\nn0ynRJdCYXgQpZpGpGzCxSWUwMAEggIT8PAYoJLBb6hoqGBn3k6SspPYmbeT6sZqHIQDcd3iGBdq\nLPSjvKLa7foFtQVsSNvAurR15Nbk4uHkwY3RNzIrdha9fVs5dV9KqM7/pSZfaCrwS04bCw8wFuR+\nMcZCPqgvBJq+e0W0S9OD1OkoeO45KlauQjNxIiEvv4y9pvN0Dmu1xZSU/kBJyTbKynZiMGixt9fg\n73/oa6EAACAASURBVDcBf//J+PmNx9HRy/wXbqw1JvWSVCg5Y/pKNX7ptb8c5+YH/pcmhljwjjAm\ncRtlkT6A9tDaJqDnVv8RjUM5PXJ2ElVXgqbvSMpDfCir2o+UOlxdIggMMiYDjaav1SYD2WRAX92I\nvbdzu8YopSS1IvXnDtyjxUcxSAO+Lr6MDf3/7Z15mBxXea/fU91dvffsM5p9JM2MbMkblmzZYFuO\nLS/YbFry3EDCDSS5LAEuCQkXCNyEcAmQJyZAQmIWA5cbTEiuJRtfMGDLNpKNF8myZbRYGkmj2Wc0\ne+/d1V117h9V05rRjKTRbD1LvXrqqaru01WnRt3f75zvfOc7t7Kldgs3V9684OGbhjTY37ef3Sd3\ns6d9Dxkjw/qS9Wxv3M5b17yVkBqa+oOpiOm+mdCqPwqp0XNlglWWkR/Xqi9tBpdnYR5uHMM//jFn\n/+5LuNesoebBB1FrFnBweA6RUhKPtzA4+DQDg08TiRwCwOOpprR0K2W5UE01PxU0dAh3wkDLecLQ\nAolx3miH22wIlDZZPQdLGEoaQV38Ar2iBSCVTvJP7/9dFF0yWKDRU5akpySJK5ikqbCaaytrqBZn\ncaVPATpeb4PpJqq4n4B/Xd7EQOoGmbMJMt0xtO4YWleUTG8cdIlaHyJ0Vz2exsI5u18qm2J/3372\nde1jb9de+uJ9AFxZfCVbardwW/VtbCjdMGkAN1+E02F+1vozdp/cTctICx6Hh7vq7mRb2Q1syhiI\ngTfOte4nuG+Cpvsm16LfYJ4vsu5//IUX6Poz0w1U881/xrdxY76rNC0MI8Po6IGc0U+lOgEIha6l\ntPROykq3Lo1QzcSwJQYnJgrDSNvEAfSC2smupNJmCJTnNXpqPCtaAKRh0Hf6JKcPHeDkqy8zfKYN\npMRwSkaK4pwuT9NRlsQIZLnGq3NjQNDgSqMIyDpK8RTeQn3VTupLb5q3L63UJdmBBFpXDK07ahr9\nnjhkzS+acDtQqwO4agIoPhfxF3rQIxruNQWE7q7H3TCzbnNfvC9n8Pf37ielp/A6vdxUeRNbarZw\na82tlPsWYYidlBDpgf5jyL4jHOs7wK7wcX7hSBNTFOozGd4VS/BOdRVl5VdNbNUX1i2aH+alSJ85\nQ9eH/xStu5vKz3+ewh3b5/V+yWyS1nArDaEG/K7pt2wzmQhDw3sZHHyaoaFfk81GzVDNoreYoZql\ndyyfUM1sGoZbTTE4v+eQiZ8r5y4YJwzjeg5FDeaA9QKyogXgfFLxGB1HXqft9VdpO/gi0VFzeoLH\nZ0BzNUO1PjpDvXiNFq5U4zS6DRQBZzMOulhFxnctqwqvY03BGtYUrqE6UH1ZYYrSkGQHk2aLvsts\n3Wd6YsiMZexVB65qP2p1ELUmgKs6gLPEi1DOGS2ZMYjt7yX6bCdGLIO7uYiCu+pRa4MXvbdu6Bwe\nPMzerr3s69pHy0gLANWBarbUbOG2mtvYtGrT/A2wzoRU5JzLZnz0TSp8rkyoGsrXkyxr5ilVsCva\nwqsjx3EIB7fW3MqOph3cUn3L4g0nvQh6OEz3n3+C+AsvUPy+91H+yb+ck8HhjJHh5MhJjgwe4ejQ\nUY4MHuH06Gl0qeNz+rhvzX3sbNrJ+pKpXaLJZGeulT86uh8ps7hcxVYr/06Ki9+y7FfPmsBYo2R8\nb2HwhHkc7T1XTnFC8ZqJkUml66C0ETzzMP6BLQAXRErJcGc77U98m7aDL9AZ9ZGVDhxOJ1Xr1lO+\n4Qr0WoWo8goydoCg3ocQ0K0JDiWcvJZ0EDbc1Ifqc4KwpsDc6kP1uBU32aGk2aLvstw4PXGkpgMg\nXAquqoBp6GuCqNUBnKUTjf3FMDSd+Iu9RPd2YiSyeK4sJnRXPWrVOd98OB3mhZ4X2Ne1j+e7n2c0\nPYpDOHhT+Zu4reY2ttRsYXXB6vx3yfWM+WM539iPj+BwhyZG34y5b7xFky53JnyGR089yuOnHmco\nNUSZt8wMJ23cRl2obgEfbPbIbJazX/l7Rn70I/xbbqP6q1/FEZj++IshDdrCbRwZOmIa/MGjHB8+\njmaYg90F7gKuKrmKDaUbWFuwlhd6XuBXbb8ipae4ovgKdjbt5K2r70Wm23KpF2LxEwD4/U05o29G\n1i3dwdJ5IxWBoZPnhGHAEobh0+acjDECqyYPQJetMxs4s/h92gIwHZIjZJ/+Ct37/i9tiVLajDUM\nDpnpCvyFRdRf8yZqr1mNd1U/g+EniVkDWgmllDN6MS9GMowMSRoTtTSm6mhK1dOUrsOnm4OIhkOi\nlzvw1RURqCtBrQngLPNN29hfDCOdJfabHqL7upGpLMY6Dy81tfCL2B5e638NXeoUugu5pfoWttRs\n4eaqmylwz09rY9oMtMCJn58blB04AUbGfE9xQknTFNE3tZf9Q8gYGZ7reo7dJ3fzXPdzGNJgU8Um\ntjdt5676u/A4F36Qd6aM/OQ/6PviF1Eb6ql98EHU2snzIqSU9MZ7OTx4mKODRzkydIRjQ8eIW+4J\nr9PL+pL1XFVyFVeVmka/JlAzqQEQ0SI8ceoxXmn7Nwqz7WzwGoQcElAoLLyBstKtlJbegc/XsABP\nvkzRMzDSft4AtDXmML6H6/LDqqvgj341IyGwBeByGGiBX/0VnHqKWKCZtpr30HY2Q/vhQ6SiERCC\nioa1rLlqHYHyQRLKy8SVNwDwhFcTPHsD/oEbSLj9dATOctR1kpd4jdOuTgxhunlKvaWsLVjL6oLV\nE3oNpd7SGbXE03qaV/pe4cXW3+B/LcudfZvwGG5eLW1h+AaD66/czNWlV+PIdyibYcCpPfDyg3D6\nGfO1UM3U0TfOuY8MORs/y+OnH+fRU4/SGe0k6Apy35r72N60nfUl6+f8fvNB/KWX6fr4xxFCUP1P\n3yB19dqcC2fMnTOcGgbAqThZV7TONPQlG7i69GpWF6y+4PdASklaO8vw0D4GcqGaKYTio58ynhka\n4vWETlWoiZ3NO3nbmrflvyGxHJES4gPnjS8k4e1fn9HlbAGYCS1Pwq/+Cjl4Er3uXaTX/TmjnTqJ\nM8M4IwouTANlSJ1osIv0msOkKn5LUph+9VDoOmvS2VtxqRV0x7ppDbea22grZ8JnaA235pKiAQRd\nQVYXrs4JwthWFaia9KPtT/TzXNdz7O3ay0u9L5HMJvE4PGyu3MwdpVvY3H4lHAgjswa+6ysI3VmH\nszhPrd10FA79O+z/thmPHVgFN/wJbPxDM1pigTGkwSt9r7D71G6eansKzdC4ovgKtjdt577V9y1a\noxbVohwbOsapw8+x+ks/IdQf56F7FJ6+TkEgWFu4lg0lG7iq1GzdNxc1ozomCqmUkkxmiESijWSy\nnUSijURy7LgdXTe/jx53FaVlWykr3ZoL1Yxn4vzizC/Y1bKLI0NHUBWVuxvuZkfTDjZWbMy/G9Fm\nSmwBmCZSSvSIZg3ORtE6I2TahzA0a/BQGLgqfKi1hYhyF4PxbtraD3Hm8EEiA2bem7K1RVRf70Qt\n7UQzzOUOCgqup9wSA4971YT7DSQHaA23cnr0dE4UWkdbGUoN5cq5HefGGUq9pRw8e5A3hs1eR6W/\nMjcD98ZVN05waehRjejeLmIv9YAB/k0VBO+ow1m4QIO8w2dg/3fhtX+DdASqN8LmD8P6d85LC38m\nhNNhnjjzBLtP7ub48HHcDjdb67eyvXE7m1ZtylvYayqb4vjw8Qmt+7ZIW+79RmcVf7o7Sc3RATI7\n7mHt576A32vOg8gZ+WQ7yUQbCcvQJ5NtE4w8gBAOPJ5qfN4GvL56fN4GCotuumQI9PHh4zzS8gg/\nb/05sUyMhlADO5t38va1b6fYs7hCalc6tgBcAD2imYa+K2YN1EYxYmN+aHCV+3HVBFDLQO35Ca4T\n30R4ffA7n4WN7zen/mNlduztNiOLXn+VzmOHyabTeIp06m50E6gdxHD0AoLCgk2UV9xHedm9Fw2N\nC6fDEwRhrPdwNn6Wq8uuzhn9psKmS7a89EiayLOdxPebsf2BzZUEb6/FEZoHIywltD0HL30LTjxh\nzqBc/y646cNQY34HdT1BOj2AbiRRXcW4XEWLIm/7saFj7D65mydanyCaiVIbrGVb4zbe2fjOeQ2H\nzRpZTo+e5sjgEdN3P3SUUyOnyEpzgLDUW5obpL269Go2lGygwF2Alhyg53tfYviVJ1A21uK4tZlU\ntodEom1KI+/11uPzNZh7bwM+XwMeT82s/vaJTIIn25/kkZZHeH3gdZyKk611W9nRvIMbV924aOaN\nrGRsAQD0mGYa+q6oObGqO4YRGZvyD85yH2p1ALUmiKs6gKvSj6Ke5yvtOwK//LRp4MrXwz1fgrW/\nM+le2UyG7uNHaXv9Vdpff5WBjjbcBWnKNmQoboqjeIYBQWHhjVSU3095+T2o6vQSpkkpZ9zVzo6k\niD7TSfxgHygKgZsrCW6pwRGYvRBILUHm9R+ivf4D0rFWtGAIrWET6Yo1pEmgaQNo2oBp+McZpzGc\nzkJUtcTcXCW41GJUl3nusl4be9/pLJhXd0Mym2RP+x4ePfUoB/oOoAiFW6tvZVvTNm6ruQ3XLAym\nIQ06Ih0cGTKjcY4MHuH48HFSegqAoBo858Yp3sC6wmoCJEwXTbKNZKI957LJZqPjLgzOiItg5XX4\ni6/IteZNI1+9ILNtT46cZPfJ3Tx++nEiWoTaYC3bm7bzrsZ3Lfv03vOJHtPIDqdw111gpvslWNEC\nILMGfQ+8gj5q5fwQ4Czzolabhl6tCeCqCkw29he8oIQ3/h88+TkYbYd198Pd/8vMMngBYiPDtP/2\nNVMQfvsahmOAorURSq5I4QrEMCMrNrOq4n7Kyu5BVee3C50dShJ5uoPEa/0Il0LgzdUEb6tG8U02\nbIahoWmDpLUBtPQAaa0fLW0Zc20ALdFFOt6BJuPIKSKaHA4/qlqKWy1HdZehqmW41XLc7jIUh49M\nZgRNGyKjDaFlhtA0c8tkhshkps60KYQTl6s4JxZTicT489msAdsR6eDRU4/y01M/ZSA5QImnhHc0\nvoPtjdsvmf9ISsnZxNmcC+fI0BGODR4jmjENt8fh4cqSK7i2uJErgyXUetz4ZMx01Uxl5FFMd42v\nYYLLxudrQD/cS+/H/wIpJTXf+Dr+m26a8TPPllQ2xZ6OPTzS8ggHzx7EKZzcXns7O5p3cHPlzfkP\nRljESCnRh1Kk2yKk28JobRGyg0kUv5PKz81sMuqKFgCA0Z+34gipltH3o7jnYEJQJgUv/Qvs+6oZ\nvnjTh+HWvwTPxVVaGgZnz5y23EUHGR44RMHqUYoaY7gL0iAVQoFNVNduo6zsblyuuUv3kKuDlOh6\nnHhvB6MvHSHe1YHuj6Cs1ZHlSTLZIdPQawMXNMIuRwh3WkeNjuLWDNRAA86q21CKr0PIEEL3IzM+\ndA20dAotmSSTSqKlUtY+iUBQVFlNcXUtJTW1+AoKJ3zBDSNrCkTGEohxIjGVYOh6Ysq6Ohw+XOPE\nwexhlEwpIKY7avL3I2tkeb77eXad3MVzXc+hS53ry6/PhZP6XD5GUiM5Qz/WujfHciQhh4Pri6q5\nMlRKvddLkZLBqQ9d2Mh76/H6GixjX4/X24DXW3PRlrzW2Unnhz+MdqaNVZ/7LEXvfve0vg/zSWu4\nld0tZq9gJD1Clb+KbU3b2Na4jQp/Rb6rl3ekLsn0xki3RdDawqTbIjk3tPA6cTeEcDeEUBsKUGuD\nMwobX/ECMK9E++DpL8Chh8FfDnf+NVz3+9POFplOJOg4+jrtrx+kp20fzqI2CtdEcBdkkFLB67qa\nuvqdrKq6/5KZEqU00DLDVgu9n3Supd5vtd7PvW4YyUmfF4YTh1aAIgqQTj8YfqTmRdfcZJMqmbhC\n5uwQWk8fWjKJJl1kHEE0w0EmrSGnuciIEAqq14uuZ8mmz2VjdPv9phhU11JcVZM7DpWXo0yj1ajr\nCTRteKJgWEIxSUAyw0iZnfI6LlfRRQUjYSjs7X2Nn7Y9w8lIFwFXkAJ3iNFEN6VOg3KnpDFQQL3H\nS4kzi6qHkca4NAEoeDxVViveNPCmb74Br7caRZn5IL0ei9H9F39BfO8+it7zHir+6jMIZ/5nQGu6\nxjOdz/BIyyO83PsyilC4rfo2djQv3VnaM8HQdLTOKNqZMOn2CFp7NDcx1FHkxt1QgGoZ/bmaJ2QL\nwELQfRB+8Wno2g+V18K9fw/1N1/WJaSUjPb10HroIF2n9pA0DhCqH8EdyiANgVNfR1nZVoSQpNP9\naJlBMtkhdGMEXYaRIgZishE2Mk70tJtswokWd6DFBFrcQTbhJJNw5vYhWclVRbdS5Wskpcc5Pvoy\np6KvoahOVIeOqsdxoeFyq6gltbjKVqP6g7g8HlSPz9p7UL3WsduDy+tD9XhwebyoXi8ujwenS0UI\ngZSS6NAgw92dDPd0MdzdyVB3J8PdXSTC5zJ1OlwuiiurKaqupaT6nDAUVVbjVGfm25bSIJuNXFwk\nxh1ns+ELXMlBGhWFLC4y414XE1vy41w2Zkt+/iKxpK7T/8BXGf7BD/C/+Waqv/Y1HAWLJ7S1M9LJ\nrpO7eOzUYwylhij3lbOtcRvbm7ZTFajKd/XmFD2mobVHLJdOhEx3DAwJAlwVftTV51r4zoL5+U7Y\nArBQSAmHH4E9fwORbtiwHe76AhTObCWrscHkM2/8jNHor3GXdqIGzVarNCCbdJgGPGka8EzCiaF5\nIOsHI4BiBFGUQlQ1YBlnr2mIzzPIqsdrvWe+7hgVZF8eJdsWR3ElCImH8YufI5puN8M4194x70vx\nJWNRhrvHi4K5hQf6zb8zZk+ioLyCYksUiqtrzN5DdS0e/9ymqjYMLTdeMZVgKIo6oUXv9dbOq5Gf\nDqO7dtP7+c+jVlVR8+CDuNesBsyGRiKRIBqNTrkZhpWXynLHjd9P9dpMyxgY9MZ6aQ230hs38+Ws\nCqyisbCRmmANilBmdU9FUfD7/QSDQYLBIIFAAL/fjzJP310pJfpwynLnmD787IDV03YK1Jqg2cJf\nHcJdF0LxLkyvxxaAhUaLw2++YW4Ab/m4uc0yd3hsZIiOlr04lABebxluX9Ay2mMtcPe0XCUXRc+a\nKRpe+hbptjBh/Q/R9PU4ggrBrWvwb6pAOPIX2pfR0oz0dFvC0JXrPYz0dKFnz7l0/IVFOTdSzq1U\nU0OgqGRZT1hKp9NEo1EikQjRaJTh48fp/eUvSaoq+hVXkBCCaDSKruuTPuvz+QgEAjisZHNjtmD8\nfqrXZlN27FiXOlpWQzM0pJQoKDgVpxlxZZmk6VznUgghCAQCBAKBCcJw/rHf78/9HS6ENCSZ3njO\nd59ui2BEzchC4XFaLXurhV8TRDjz87uxBSBfjHaavYEju8yETlv/Fq7euTjTESeGzQlb+79rLpJR\nWAc3fhB53e+T7obIU+1oHVEcxR5Cd9The1M5wrF4nsMwdML9Z01h6DLdSMM95j6dOOd/V73eycJQ\nXUthxSqURbwEYyaTIRaL5VrpYwb+/E3TtEmfdbtceCJR3JEIRY1rKb3mmpzBG785F8FYQW6wvWUX\n+7r3YUiDzZWb2dm8kztq75g0s3kqxgRB13Xi8XjubzP+7zd2HIvFiMfjU17n/N5DwOfHm3HhiSq4\nhg3UPh1v2oGCgqPQbRn7AtN/Xz43/vu5IB+Lwt8LfANwAA9JKb9y3vvCev8+IAG8T0r56qWuu+QE\nYIz2F+GXn4Le16F2M9z7ZXNW7GKg/zi8/C347X9AJgENt8LmD8G6t05YBk9KSerECJGn2sl0x3CW\negltrcN7Tdmi+aJPhZSS+OjIea4ks+cQGxnOlVMcTooqqya4kYqraymuqsblnr8UGucbqQsZ+GRy\n8qC9w+EgGAwSCoWmNOhjm9vtRo/F6fnkJ4k9+yyFv/dfWPXZzyJc+Z98dzH64n08duoxdp/cTW+8\nlyJ3Ee9Y+w52NO9gdcHqObuPruvEYrFJAhEZCRMZGCUajhBLxUnqaeQUX3Wf10swFJqyJzF+78rT\n33uh1wR2AC3AXUAXcAB4t5Ty2Lgy9wEfwxSAzcA3pJSbL3XtJSsAYCZCO/SwGTEU74dr3wNb/waC\nqy792fmoy6mn4KUHofVZc8m7a37XNPyrrr7oR6WUpI4OEX6qnezZBM4KH6Gt9Xg3lCxqIZiKdCLO\ncHeXKQzWIPRwdyejfX0TIppCZeVWb6FmnDDU4AtdeGD1Un72MQMfj8cnuS/G3BRjxuRCBt7r9V6W\nO0vqOgNf/zpD330I3+bNVH/9aziLJqfSXmzohs6LvS+yq2UXv+78NVmZZWPFRnY07ZizjK5SSvSR\ndC72Pt0WJttvia7D9N+7GgJkV6mkCyTxTHLKHsXY8VR21OPxXNTtNHaszjCw4UIstADcDHxeSnmP\ndf4ZACnll8eV+Tbwaynlv1vnJ4DbpZS9U1wyx5IWgDFSEXjuAdP4OlS49RNw00cWZu3ZdBQO/Rhe\n/raZizxYCTf8sZnWwn95MzWlIUkeHiSyp53sQBJXpZ/Q3fV4rihe8j72bCbDaG83wz1duaikoe5O\nRnq6yWppJCCdKq6CQnxlq3AVFCLcXrIINF0nqWVIJJMX9LOfb8jPN/DzOVAJMPrYY/T9z7/GWVlJ\n7YP/invthScxLjYGk4O5XkFntJOQGuLta9/OjqYdNBU1Tfs60pBk+uI5Y6+1RdAjY/57B+76EOpq\n052jVgcRrun/fxiGkRP/KUUiHDbPE4ncgPt4HEicwsBp6Dj0DEpWwyUMPvLlf552Hcaz0AKwE7hX\nSvkn1vl7gc1Syo+OK/Mz4CtSyuet86eBT0kpJ1l3IcQHgA8A1NXVbWxvb59V/RYNQ6fhyf9pDrgW\n1sPdX4Qr3z4/4wPDrVZSth+ZSdlqbjBb++vfOevl6aQuSRzqJ/J0B/pwCrU2SOiuetxNhUtSCMyF\nzOOEw2EikQjhcHjC8ejIiNlqP/+Duo6S1RDZDCKjoWQzCD2LV3XljH5BQSHBoiL8hUX4Cs392KZ6\nfQv690q8+hpdH/sYMp2m+mv/SODWWxfs3nOBIQ329+1nV8su9nTsIWtkubbsWnY27+SehnvwOifO\n/pYZHa0zRro9TPpMBK09gkybAq0EXag1XpxlTijU0R0JMvEEmUSMTDyOlkiQTsRIJaKkknG0ZAIt\nnSKjpchoGnomg57Nomd1DEPH0A10KZESDMY2gSEEuiIwLHGXAA4HhlNFOl1IpwvD2pvH515Xshn+\n+ktfZiYsaQEYz0x7APF4HL9/dhE480brr+GXnzEXRWm4Fe79irn4w2yREs7sNZOytfzS9Odv2GaG\ncdbM/fiD1A0SB/uJPNOBPppGbbAWrl879zOZZ0MqlZpk1McfRyKRSS13p9NJKBSioKCAgoICQqEQ\noUCIoNtHwOkjoHhxZCWpZJxUPEYqGSUZj5KMRUjGwiSiYeKRMPHoCInwCFk9g5Q6BtLaGzhdqiUK\nhTlR8BVMFAnztcIZz304n0x3N50f+SjplhYqPv0pit773kUn2jKbRU8kMKJxjFgCPZFAj8bRRiOk\nohG0SJxYdISuwTb6R89iaBncUiWkBPE5QvhdqwiqVQTdq3IzvKPpfoYTHQwmuxhMdRIzouhCmTKV\nyXRQDAMhJYo0AInAjPMXAoQCKALhEAiHA+FUUFxOHC4XituNw6Picntx+by4vH48/gCeQAhPMIQv\nWEywsAR/QQluXyGhwpm561a0C8gwDB544AE8Hg/r1q2jubmZurq6S4Z4LSh6Fg7+AJ79O3MloOv/\nEO743GW7ZQDQEnD4P003T/8x8JXCpvfDpj+GUOXc1/08ZNYgfqCPyDOdGFEN99oCQnc34K6fWSKr\nyyGTyUwy5ucb+POjZIQQpkEPhgj5ggTdfgIuHwGHlwAe/LobNa0gE1mMeAY9nsGIZ5Cpye6d2SCt\nfwaGKQpSRzfMvcTAkAZSGhjolkFRTGPidOJQnaZRcbtwulWcbjdOjxunR0VxOnIGCIcwx2kcAqEo\n4BCQzTD62G5Sx47hu+F6CrdvQygOpCFBl0jDsPYSqUsYv7fKYEhkVsfQskgtY24ZHZnJIrM6MqOD\nbmBkDbOcbpjXM8wmskRgjq4KQEEIBTG2t7aZYkid4VQPQ6lOBlNtDKQ70WQCQ0ikIpEOAU4FXAo4\nHQjVhXA7UdwqDo8Hp9eLw+dF9QdQA0HcwRCeUAH+UBE+b4iAL4Tf5cfn9OF1efE6vbNKFjgfLLQA\nODEHge8EujEHgd8jpTw6rsz9wEc5Nwj8T1LKGy917ZkIQDab5dVXX+XEiRO0tbWh6zoej4fGxkaa\nm5tpbGzE51ski1cnhmHv35vuGjUAt38Kbvhv08udH+6CAw/Bwf8NyRGouBpu+hBctXNhxhfOQ2Z0\nYi/1mesVxzJ41hWZ6xXXXHzh+guh6zrRaPSiBj6RmJwLyO/xEfQGCKpWa1148Rtu/FkVn+bCk3Ag\nEzpkL5DGwiFQ/C4cfheKtZ07dubOcSrnjKMuJxvQ842nLsEwkPpkgyp1AwyJkdHJpjWyqTR6WiOb\nzqBrGYxM1tyyOlI3ryEkKDgQQkGxjKciFBThRBEOc1KV9W8ukNIUqtzeOCdUpoiZe33ca1afxxS1\nCeV0pJQ5sQOJEGbWW6EIFIdAGSd2DtVlCZwbp8+L0+/DFfDj8vtw+Ty4vF7SSoYTsZPoZQ68Xl/O\nQPucPrxOc++apftzqZCPMND7gK9jhoF+X0r5d0KIDwFIKb9lhYF+E7gXMwz0/Zdy/8DsB4HT6TSt\nra2cOHGCkydPEo/HEUJQV1dHc3Mzzc3NlJbObFnGOaX/uLks5emnzbVx7/0yNN01uZyU0PmyGcZ5\n7HFAwhX3m26e+jcvivkGhqYTe6GH2L4uc+H69SWmEFSec8mNDZpdzDUzVWSF26GarXXFix8PAd2N\nT3PhS7sISDd+6cHBxNajUB0ogXGG3OdECYwz6j7XhHPhduT/+zANtFSSxOgo8dER4uER4qMjClYO\npAAAC9dJREFUJEbNvbmNEg+br5mdCEskLNFQXW48qgfXSBRd6mQUSVZINEWgi3MG3ZCGZaQnIhC4\nXE5Ul4pLdaO6Pbi9XlSvD9Xvxx0I4g4GcYcKzFa0z2++5zPLuL0+VJ8Pl9uzJP7eSwl7ItgUGIZB\nT08PJ06coKWlhbNnzwJQXFycE4P6+vr8uYqkhJNPmuMDw6eh8S5z/YGyZsim4eijZiRR7yHwFMD1\n/9XsLRTV56e+l8BImQvXn33uNH3aMEPlaYbdCSKxCNFkDP28aAgHyrnWuu4mgGnQA9KD3zLuqnCa\nBtw3zqAHXOfOxx0rARcOn+uyojmWI9IwSMVjOWHIiUTYEo+hQRRFwR0ImEZ7zFB7fbh9PlTveIPt\nz73mVN224V6k2AIwDUZHR2lpaaGlpYUzZ86g6zputzvnKmpqasqPqyirwf7vmK6hTAKufAe0PW/O\nJShths0fhGvfPes0E/OBlJKhoSE6Ojpy2/CwOfnKIRVKZJCg9FiG3Y1feAl5/AT9QXwBP46AOsH1\ncs794sy11pfa3AMbm4XGFoDLZMxVNCYIY66i2tpampubWbdu3cK7imID8OwX4bWHzVXINn8Q1sx/\nUrbLIZvN0tvbS0dHB52dnXR0dOT88j6fj7q6utxWHipF702geJ1Lzt1iY7OUsAVgFoy5isbEoK/P\nXFe3qKgoJwZ1dXULl0dFykXh2wczpHLM0Hd0dNDd3U3WSshWXFw8weCXlCzvJGw2NosVWwDmkHA4\nTEtLCydOnJjgKlq7di3r1q3Ln6toAQiHwxPcOWPjJkIIKisrJxj8QGBu0zHb2NjMDFsA5glN0yZE\nFcVisQmuoubmZsrKypZky9cwDAYGBiYY/HDYXBRFVVVqampyxr66uhq3O7+5721sbKbGFoAFwDAM\nent7c72D811FY1FFiyHl7lRkMhl6enpyxr6zs5NUKgVAIBCY0LqvqKhYXBPpbGxsLogtAHlgzFU0\nFlWUzWZRVXVCVFE+01MkEokJ/vuenp5cCoTS0tIJBr+oqGhJ9mJsbGxsAcg7Y66iMUGIxWIAE6KK\n5tNVJKVkdHR0gjtnYGAAAEVRqKqqyhn72traxZs3ycbG5rKxBWARMd5V1NLSQm+vmf6osLAwJwaz\ndRXpuk5/f/8Egx+NRgFwu93U1tZO8N/na6EKGxub+ccWgEVMJBLJiUFra2vOVTQ+quhSLXJN0+jq\n6soZ+66urlzSs4KCggnunLKysnnNNW9jY7O4sAVgiaBpGmfOnMkJwlirvaamJpfJtLy8nHg8PqF1\n39vbm8uTU1FRMcGdU1i4uNIx29jYLCy2ACxBpJQToorGXEUejycXneNwOCaEY9bU1OD1ei92WRsb\nmxXG5QjA4oxRXIEIIaiqqqKqqorbb7+dSCTCyZMn6ezspKysjLq6OiorKxdtWKmNjc3Sw7Ymi5RQ\nKMTGjRvZuHHuV/OysbGxAbBHB21sbGxWKLYA2NjY2KxQbAGwsbGxWaHMagxACPEPwNsBDTiNudTj\n6BTl2oAooAPZ6Y5Q29jY2NjMH7PtATwFXCWlvAZzYfjPXKTs70gpr7ONv42Njc3iYFYCIKV8UkqZ\ntU5fAmpmXyUbGxsbm4VgLscA/gj4xQXek8AeIcRBIcQHLnYRIcQHhBCvCCFeGUtgZmNjY2Mz91xy\nDEAIsQdYNcVbn5VS/tQq81kgCzx8gcvcIqXsFkKUA08JIY5LKfdNVVBK+R3gO2DOBJ7GM9jY2NjY\nzIBZp4IQQrwP+CBwp5QyMY3ynwdiUsoHplF2AGifYdVKgcEZfnaxsVyeZbk8B9jPshhZLs8Bs3uW\neill2XQKzjYK6F7gfwBbLmT8hRB+QJFSRq3ju4EvTOf6032IC9z3leUy4LxcnmW5PAfYz7IYWS7P\nAQv3LLMdA/gmEMR06xwSQnwLQAhRJYR4wipTATwvhHgd2A/8XEr5y1ne18bGxsZmlsyqByClbLzA\n6z3AfdZxK3DtbO5jY2NjYzP3LOeZwN/JdwXmkOXyLMvlOcB+lsXIcnkOWKBnWdTrAdjY2NjYzB/L\nuQdgY2NjY3MRbAGwsbGxWaEsOwEQQtwrhDghhDglhPh0vuszU4QQ3xdC9AshjuS7LrNFCFErhHhW\nCHFMCHFUCPHxfNdppgghPEKI/UKI161n+dt812k2CCEcQojXhBA/y3ddZoMQok0IcdiKRlzS68gK\nIQqFEI8IIY4LId4QQtw8b/daTmMAQggHZlK6u4Au4ADwbinlsbxWbAYIIW4DYsD/kVJele/6zAYh\nRCVQKaV8VQgRBA4C71qi/y8C8EspY0IIF/A88HEp5Ut5rtqMEEJ8AtgEhKSUb8t3fWaKlXF4k5Ry\nyU8EE0L8EHhOSvmQEEIFfFNlWZ4LllsP4EbglJSyVUqpAT8B3pnnOs0IK1XGcL7rMRdIKXullK9a\nx1HgDaA6v7WaGdIkZp26rG1JtqKEEDXA/cBD+a6LjYkQogC4DfgegJRSmy/jD8tPAKqBznHnXSxR\nQ7NcEUI0AG8CXs5vTWaO5TY5BPQDT0kpl+qzfB1zJr+R74rMAdNOOLnIWQ0MAD+wXHMPWRkU5oXl\nJgA2ixghRADYBfyZlDKS7/rMFCmlLqW8DjP9+Y1CiCXnohNCvA3ol1IezHdd5ohbrP+TtwIfsVyo\nSxEncD3woJTyTUAcmLexzOUmAN1A7bjzGus1mzxj+ct3AQ9LKXfnuz5zgdU1fxa4N991mQFvAd5h\n+c5/AtwhhPhRfqs0c6SU3da+H3gU0x28FOkCusb1Kh/BFIR5YbkJwAGgSQix2ho8+T3g8TzXacVj\nDZx+D3hDSvmP+a7PbBBClAkhCq1jL2bAwfH81urykVJ+RkpZI6VswPydPCOl/IM8V2tGCCH8VnDB\nWPLJu4ElGT0npewDOoUQ66yX7gTmLVhiVrmAFhtSyqwQ4qPArwAH8H0p5dE8V2tGCCH+HbgdKBVC\ndAF/I6X8Xn5rNWPeArwXOGz5zgH+Skr5xEU+s1ipBH5oRZwpwH9KKZd0COUyoAJ41Gxn4AR+vMQT\nTn4MeNhqxLYC75+vGy2rMFAbGxsbm+mz3FxANjY2NjbTxBYAGxsbmxWKLQA2NjY2KxRbAGxsbGxW\nKLYA2NjY2KxQllUYqM3KRQhRAjxtna4CdMwp9QAJKeWb5/h+PuC7wDWAAEYxJ4Q5gfdIKf91Lu9n\nYzMf2GGgNssOIcTngZiU8oF5vMdngDIp5Ses83VAG+Y8gZ8t9QyuNisD2wVks+wRQsSs/e1CiL1C\niJ8KIVqFEF8RQvy+ld//sBBirVWuTAixSwhxwNreMsVlKxmXZkRKeUJKmQa+Aqy18tL/g3W9T1rX\n+e3Y+gFCiAYr3/vDVs73R6xeBVa9jlnl503EbGxsF5DNSuNa4ErMVNutwENSyhutRWo+BvwZ8A3g\na1LK54UQdZgzy6887zrfB54UQuzEdD39UEp5EjNx11VWYjKEEHcDTZi5aQTwuJWorANYB/yxlPI3\nQojvA38qhPgBsA24Qkopx9JO2NjMB3YPwGalccBanyANnAaetF4/DDRYx1uBb1ppKx4HQlYm0xxS\nykPAGuAfgGLggBDifJEAMy/N3cBrwKvAFZiCANAppfyNdfwj4BYgDKSA7wkhtgOJ2T2ujc2FsXsA\nNiuN9LhjY9y5wbnfgwLcJKVMXexC1sIwu4HdQggDuA8z4+l4BPBlKeW3J7xorotw/gCctPJZ3YiZ\nBGwn8FHgjks/lo3N5WP3AGxsJvMkpjsIACHEdecXEEK8RQhRZB2rwHqgHYgCwXFFfwX80VgPQghR\nLYQot96rG7fe63uA561yBVaivD/HdFnZ2MwLdg/AxmYy/x34FyHEbzF/I/uAD51XZi3woJXqWgF+\nDuyy/Pa/EUIcAX4hpfyk5Rp60cpWGQP+ADNM9QTm4iXfx0z5+yBQAPxUCOHB7D18Yp6f1WYFY4eB\n2tjkAcsFZIeL2uQV2wVkY2Njs0KxewA2NjY2KxS7B2BjY2OzQrEFwMbGxmaFYguAjY2NzQrFFgAb\nGxubFYotADY2NjYrlP8P4hqRF1/LqxMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0681d66e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot 10 paths\n",
    "plt.plot(a.T.iloc[:,idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Optimal Hedge')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(Pi.T.iloc[:,idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Portfolio Value')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the optimal hedge $a_t^\\star$ and portfolio value $\\Pi_t$ are all computed, the reward function $R_t\\left(X_t,a_t,X_{t+1}\\right)$ could then be computed by\n",
    "\n",
    "$$R_t\\left(X_t,a_t,X_{t+1}\\right)=\\gamma a_t\\Delta S_t-\\lambda Var\\left[\\Pi_t\\space|\\space\\mathcal F_t\\right]\\quad t=0,...,T-1$$\n",
    "\n",
    "with terminal condition $R_T=-\\lambda Var\\left[\\Pi_T\\right]$.\n",
    "\n",
    "Plot of 5 reward function $R_t$ paths is shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Compute the optimal Q-function with the DP approach "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coefficients for expansions of the optimal Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ are solved by\n",
    "\n",
    "$$\\omega_t=\\mathbf C_t^{-1}\\mathbf D_t$$\n",
    "\n",
    "where $\\mathbf C_t$ and $\\mathbf D_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$C_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\Phi_m\\left(X_t^k\\right)}\\quad\\quad D_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\left(R_t\\left(X_t,a_t^\\star,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\right)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function *function_C* and *function_D* to compute the value of matrix $\\mathbf C_t$ and vector $\\mathbf D_t$.\n",
    "\n",
    "**Instructions:**\n",
    "Copy-paste implementations from the previous assignment,i.e. QLBS as these are the same functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def function_C_vec(t, data_mat, reg_param):\n",
    "    \"\"\"\n",
    "    function_C_vec - calculate C_{nm} matrix from Eq. (56) (with a regularization!)\n",
    "    Eq. (56) in QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    Arguments:\n",
    "    t - time index, a scalar, an index into time axis of data_mat \n",
    "    data_mat - pandas.DataFrame of values of basis functions of dimension T x N_MC x num_basis\n",
    "    reg_param - regularization parameter, a scalar\n",
    "    \n",
    "    Return:\n",
    "    C_mat - np.array of dimension num_basis x num_basis\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 5-6 lines of code)\n",
    "    # C_mat = your code goes here ....\n",
    "    X_mat = data_mat[t, :, :]\n",
    "    num_basis_funcs = X_mat.shape[1]\n",
    "    C_mat = np.dot(X_mat.T, X_mat) + reg_param * np.eye(num_basis_funcs)  \n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    return C_mat\n",
    "\n",
    "def function_D_vec(t, Q, R, data_mat, gamma=gamma):\n",
    "    \"\"\"\n",
    "    function_D_vec - calculate D_{nm} vector from Eq. (56) (with a regularization!)\n",
    "    Eq. (56) in QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    Arguments:\n",
    "    t - time index, a scalar, an index into time axis of data_mat \n",
    "    Q - pandas.DataFrame of Q-function values of dimension N_MC x T\n",
    "    R - pandas.DataFrame of rewards of dimension N_MC x T\n",
    "    data_mat - pandas.DataFrame of values of basis functions of dimension T x N_MC x num_basis\n",
    "    gamma - one time-step discount factor $exp(-r \\delta t)$\n",
    "    \n",
    "    Return:\n",
    "    D_vec - np.array of dimension num_basis x 1\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 2-3 lines of code)\n",
    "    # D_vec = your code goes here ...\n",
    "    X_mat = data_mat[t, :, :]\n",
    "    D_vec = np.dot(X_mat.T, R.loc[:,t] + gamma * Q.loc[:, t+1])\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    return D_vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_C* and *function_D* for $t=T-1,...,0$ together with basis function $\\Phi_n\\left(X_t\\right)$ to compute optimal action Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\sum_n^N{\\omega_{nt}\\Phi_n\\left(X_t\\right)}$ backward recursively with terminal condition $Q_T^\\star\\left(X_T,a_T=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the QLBS price to European put price given by Black-Sholes formula.\n",
    "\n",
    "$$C_t^{\\left(BS\\right)}=Ke^{-r\\left(T-t\\right)}\\mathcal N\\left(-d_2\\right)-S_t\\mathcal N\\left(-d_1\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# The Black-Scholes prices\n",
    "def bs_put(t, S0=S0, K=K, r=r, sigma=sigma, T=M):\n",
    "    d1 = (np.log(S0/K) + (r + 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    d2 = (np.log(S0/K) + (r - 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    price = K * np.exp(-r * (T-t)) * norm.cdf(-d2) - S0 * norm.cdf(-d1)\n",
    "    return price\n",
    "\n",
    "def bs_call(t, S0=S0, K=K, r=r, sigma=sigma, T=M):\n",
    "    d1 = (np.log(S0/K) + (r + 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    d2 = (np.log(S0/K) + (r - 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    price = S0 * norm.cdf(d1) - K * np.exp(-r * (T-t)) * norm.cdf(d2)\n",
    "    return price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hedging and Pricing with Reinforcement Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a batch-mode off-policy model-free Q-Learning by Fitted Q-Iteration. The only data available is given by a set of $N_{MC}$ paths for the underlying state variable $X_t$, hedge position $a_t$, instantaneous reward $R_t$ and the next-time value $X_{t+1}$.\n",
    "\n",
    "$$\\mathcal F_t^k=\\left\\{\\left(X_t^k,a_t^k,R_t^k,X_{t+1}^k\\right)\\right\\}_{t=0}^{T-1}\\quad k=1,...,N_{MC}$$\n",
    "\n",
    "Detailed steps of solving the Bellman optimalty equation by Reinforcement Learning are illustrated below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expand Q-function in basis functions with time-dependent coefficients parametrized by a matrix $\\mathbf W_t$.\n",
    "\n",
    "$$Q_t^\\star\\left(X_t,a_t\\right)=\\mathbf A_t^T\\mathbf W_t\\Phi\\left(X_t\\right)=\\mathbf A_t^T\\mathbf U_W\\left(t,X_t\\right)=\\vec{W}_t^T \\vec{\\Psi}\\left(X_t,a_t\\right)$$\n",
    "\n",
    "$$\\mathbf A_t=\\left(\\begin{matrix}1\\\\a_t\\\\\\frac{1}{2}a_t^2\\end{matrix}\\right)\\quad\\mathbf U_W\\left(t,X_t\\right)=\\mathbf W_t\\Phi\\left(X_t\\right)$$\n",
    "\n",
    "where $\\vec{W}_t$ is obtained by concatenating columns of matrix $\\mathbf W_t$ while \n",
    "$ vec \\left( {\\bf \\Psi} \\left(X_t,a_t \\right) \\right) = \n",
    "  vec \\, \\left( {\\bf A}_t  \\otimes {\\bf \\Phi}^T(X) \\right) $ stands for \n",
    "a vector obtained by concatenating columns of the outer product of vectors $ {\\bf A}_t $ and $ {\\bf \\Phi}(X) $.\n",
    "\n",
    "Compute vector $\\mathbf A_t$ then compute $\\vec\\Psi\\left(X_t,a_t\\right)$ for each $X_t^k$ and store in a dictionary with key path and time $\\left[k,t\\right]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Make off-policy data\n",
    "\n",
    "- **on-policy** data - contains an optimal action and the corresponding reward\n",
    "- **off-policy** data - contains random action and the corresponding reward\n",
    "\n",
    "Given a large enough sample, i.e. N_MC tending to infinity Q-Learner will learn an optimal policy from the data in a model-free setting.\n",
    "In our case a random action is an optimal action + noise generated by sampling from uniform: distribution $$a_t\\left(X_t\\right) = a_t^\\star\\left(X_t\\right) \\sim U\\left[1-\\eta, 1 + \\eta\\right]$$\n",
    "\n",
    "where $\\eta$ is a disturbance level\n",
    "In other words, each noisy action is calculated by taking optimal action computed previously and multiplying it by a uniform r.v. in the interval $\\left[1-\\eta, 1 + \\eta\\right]$\n",
    "\n",
    "**Instructions:**\n",
    "In the loop below:\n",
    " - Compute the optimal policy, and write the result to a_op\n",
    " - Now disturb these values by a random noise\n",
    " $$a_t\\left(X_t\\right) = a_t^\\star\\left(X_t\\right) \\sim U\\left[1-\\eta, 1 + \\eta\\right]$$\n",
    " - Compute portfolio values corresponding to observed actions\n",
    " $$\\Pi_t=\\gamma\\left[\\Pi_{t+1}-a_t^\\star\\Delta S_t\\right]\\quad t=T-1,...,0$$\n",
    " - Compute rewards corrresponding to observed actions\n",
    " $$R_t\\left(X_t,a_t,X_{t+1}\\right)=\\gamma a_t\\Delta S_t-\\lambda Var\\left[\\Pi_t\\space|\\space\\mathcal F_t\\right]\\quad t=T-1,...,0$$\n",
    "with terminal condition $$R_T=-\\lambda Var\\left[\\Pi_T\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done with backward loop!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.5 #  0.5 # 0.25 # 0.05 # 0.5 # 0.1 # 0.25 # 0.15\n",
    "reg_param = 1e-3\n",
    "np.random.seed(42) # Fix random seed\n",
    "\n",
    "# disturbed optimal actions to be computed \n",
    "a_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_op.iloc[:,-1] = 0\n",
    "\n",
    "# also make portfolios and rewards\n",
    "# portfolio value\n",
    "Pi_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op.iloc[:,-1] = S.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_op_hat = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op_hat.iloc[:,-1] = Pi_op.iloc[:,-1] - np.mean(Pi_op.iloc[:,-1])\n",
    "\n",
    "# reward function\n",
    "R_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "R_op.iloc[:,-1] = - risk_lambda * np.var(Pi_op.iloc[:,-1])\n",
    "\n",
    "# The backward loop\n",
    "for t in range(T-1, -1, -1):\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 11-12 lines of code)\n",
    "    \n",
    "    # 1. Compute the optimal policy, and write the result to a_op\n",
    "    a_op.loc[:, t] = a.loc[:, t]\n",
    "    # 2. Now disturb these values by a random noise\n",
    "    a_op.loc[:, t] *= np.random.uniform(1 - eta, 1 + eta, size=a_op.shape[0])\n",
    "    # 3. Compute portfolio values corresponding to observed actions    \n",
    "    Pi_op.loc[:,t] = gamma * (Pi_op.loc[:,t+1] - a_op.loc[:,t] * delta_S.loc[:,t])\n",
    "    Pi_hat.loc[:,t] = Pi_op.loc[:,t] - np.mean(Pi_op.loc[:,t])\n",
    "    \n",
    "    # 4. Compute rewards corrresponding to observed actions\n",
    "    R_op.loc[:,t] = gamma * a_op.loc[:,t] * delta_S.loc[:,t] - risk_lambda * np.var(Pi_op.loc[:,t])\n",
    "    ### END CODE HERE ###\n",
    "print('done with backward loop!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ -4.41648229e-02,  -1.11627835e+00,  -3.26618627e-01,\n",
       "        -4.41648229e-02,   1.86629772e-01,  -3.26618627e-01,\n",
       "        -3.26618627e-01,  -4.41648229e-02,  -1.91643174e+00,\n",
       "         1.86629772e-01,  -4.41648229e-02,  -1.15471981e+01,\n",
       "         8.36214406e-03,  -4.41648229e-02,  -5.19860756e-01,\n",
       "         8.36214406e-03,   8.36214406e-03,  -4.41648229e-02,\n",
       "        -5.82629891e-02,  -5.19860756e-01,  -4.41648229e-02,\n",
       "        -2.93024596e+00,  -6.70591047e-01,  -4.41648229e-02,\n",
       "         3.38303735e-01,  -6.70591047e-01,  -6.70591047e-01,\n",
       "        -4.41648229e-02,  -1.35776224e-01,   3.38303735e-01,\n",
       "        -4.41648229e-02,   3.89179538e-02,  -2.11256164e+00,\n",
       "        -4.41648229e-02,  -8.62139383e-01,  -2.11256164e+00,\n",
       "        -2.11256164e+00,  -4.41648229e-02,   1.03931641e+00,\n",
       "        -8.62139383e-01,  -4.41648229e-02,  -3.88581528e+00,\n",
       "        -2.78664643e-01,  -4.41648229e-02,   1.08026845e+00,\n",
       "        -2.78664643e-01,  -2.78664643e-01,  -4.41648229e-02,\n",
       "        -1.59815566e-01,   1.08026845e+00,  -4.41648229e-02,\n",
       "         1.34127261e+00,  -1.32542466e+00,  -4.41648229e-02,\n",
       "        -1.75711669e-01,  -1.32542466e+00,  -1.32542466e+00,\n",
       "        -4.41648229e-02,  -6.89031647e-01,  -1.75711669e-01,\n",
       "        -4.41648229e-02,   1.36065847e+00,  -4.83656917e-03,\n",
       "        -4.41648229e-02,   1.01545031e+00,  -4.83656917e-03,\n",
       "        -4.83656917e-03,  -4.41648229e-02,   1.06509261e+00,\n",
       "         1.01545031e+00,  -4.41648229e-02,  -5.48069399e-01,\n",
       "         6.69233272e+00,  -4.41648229e-02,   2.48031088e+00,\n",
       "         6.69233272e+00,   6.69233272e+00,  -4.41648229e-02,\n",
       "        -4.96873017e-01,   2.48031088e+00,  -4.41648229e-02,\n",
       "         1.05762523e+00,  -5.25381441e+00,  -4.41648229e-02,\n",
       "        -3.93284570e+00,  -5.25381441e+00,  -5.25381441e+00,\n",
       "        -4.41648229e-02,  -1.75980494e-01,  -3.93284570e+00,\n",
       "        -4.41648229e-02,  -1.12194921e-01,  -2.04245741e-02,\n",
       "        -4.41648229e-02,  -2.95192215e-01,  -2.04245741e-02,\n",
       "        -2.04245741e-02,  -4.41648229e-02,  -1.70008788e+00,\n",
       "        -2.95192215e-01])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "np.random.seed(42)\n",
    "idx_row = np.random.randint(low=0, high=R_op.shape[0], size=10)\n",
    "\n",
    "np.random.seed(42)\n",
    "idx_col = np.random.randint(low=0, high=R_op.shape[1], size=10)\n",
    "\n",
    "part_1 = list(R_op.loc[idx_row, idx_col].values.flatten())\n",
    "try:\n",
    "    part1 = \" \".join(map(repr, part_1))\n",
    "except TypeError:\n",
    "    part1 = repr(part_1)\n",
    "submissions[all_parts[0]]=part1\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:1],all_parts,submissions)\n",
    "\n",
    "R_op.loc[idx_row, idx_col].values.flatten()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([  0.        ,   1.42884104,   0.33751419,   0.        ,\n",
       "         1.21733506,   0.33751419,   0.33751419,   0.        ,\n",
       "         3.11498207,   1.21733506,   0.        ,  11.42133749,\n",
       "        -0.10310673,   0.        ,  11.86648425,  -0.10310673,\n",
       "        -0.10310673,   0.        ,  11.85284966,  11.86648425,\n",
       "         0.        ,   3.77013248,   0.86748124,   0.        ,\n",
       "         3.39527529,   0.86748124,   0.86748124,   0.        ,\n",
       "         3.50140426,   3.39527529,   0.        ,   2.37907167,\n",
       "         2.45349463,   0.        ,   3.21159555,   2.45349463,\n",
       "         2.45349463,   0.        ,   2.143548  ,   3.21159555,\n",
       "         0.        ,   4.22816728,   0.36745282,   0.        ,\n",
       "         3.10906092,   0.36745282,   0.36745282,   0.        ,\n",
       "         3.24065673,   3.10906092,   0.        ,   1.4213709 ,\n",
       "         2.79987609,   0.        ,   1.57224362,   2.79987609,\n",
       "         2.79987609,   0.        ,   2.24072042,   1.57224362,\n",
       "         9.05061694,   4.48960086,   5.90296866,   9.05061694,\n",
       "         3.43400874,   5.90296866,   5.90296866,   9.05061694,\n",
       "         2.3390757 ,   3.43400874,  11.39022164,   5.65090831,\n",
       "         5.15180177,  11.39022164,   3.12466356,   5.15180177,\n",
       "         5.15180177,  11.39022164,   3.59323901,   3.12466356,\n",
       "         0.        ,   3.05819303,   4.15983366,   0.        ,\n",
       "         6.95803609,   4.15983366,   4.15983366,   0.        ,\n",
       "         7.08659999,   6.95803609,   0.        ,   0.12024876,\n",
       "         0.03147899,   0.        ,   0.3970914 ,   0.03147899,\n",
       "         0.03147899,   0.        ,   2.08248553,   0.3970914 ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "np.random.seed(42)\n",
    "idx_row = np.random.randint(low=0, high=Pi_op.shape[0], size=10)\n",
    "\n",
    "np.random.seed(42)\n",
    "idx_col = np.random.randint(low=0, high=Pi_op.shape[1], size=10)\n",
    "\n",
    "part_2 = list(Pi_op.loc[idx_row, idx_col].values.flatten())\n",
    "try:\n",
    "    part2 = \" \".join(map(repr, part_2))\n",
    "except TypeError:\n",
    "    part2 = repr(part_2)\n",
    "submissions[all_parts[1]]=part2\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:2],all_parts,submissions)\n",
    "\n",
    "Pi_op.loc[idx_row, idx_col].values.flatten()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Override on-policy data with off-policy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Override on-policy data with off-policy data\n",
    "a = a_op.copy()      # distrubed actions\n",
    "Pi = Pi_op.copy()    # disturbed portfolio values\n",
    "Pi_hat = Pi_op_hat.copy()\n",
    "R = R_op.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 10000, 7)\n"
     ]
    }
   ],
   "source": [
    "# make matrix A_t of shape (3 x num_MC x num_steps)\n",
    "num_MC = a.shape[0] # number of simulated paths\n",
    "num_TS = a.shape[1] # number of time steps\n",
    "a_1_1 = a.values.reshape((1, num_MC, num_TS))\n",
    "\n",
    "a_1_2 = 0.5 * a_1_1**2\n",
    "ones_3d = np.ones((1, num_MC, num_TS))\n",
    "\n",
    "A_stack = np.vstack((ones_3d, a_1_1, a_1_2))\n",
    "\n",
    "print(A_stack.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12, 10000, 7)\n",
      "(36, 10000, 7)\n"
     ]
    }
   ],
   "source": [
    "data_mat_swap_idx = np.swapaxes(data_mat_t,0,2)\n",
    "\n",
    "print(data_mat_swap_idx.shape) # (12, 10000, 25)\n",
    "\n",
    "# expand dimensions of matrices to multiply element-wise\n",
    "A_2 = np.expand_dims(A_stack, axis=1) # becomes (3,1,10000,25)\n",
    "data_mat_swap_idx = np.expand_dims(data_mat_swap_idx, axis=0)  # becomes (1,12,10000,25)\n",
    "\n",
    "Psi_mat = np.multiply(A_2, data_mat_swap_idx) # this is a matrix of size 3 x num_basis x num_MC x num_steps\n",
    "\n",
    "# now concatenate columns along the first dimension\n",
    "# Psi_mat = Psi_mat.reshape(-1, a.shape[0], a.shape[1], order='F')\n",
    "Psi_mat = Psi_mat.reshape(-1, N_MC, T+1, order='F')\n",
    "\n",
    "print(Psi_mat.shape) #"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(36, 1, 10000, 7) (1, 36, 10000, 7)\n",
      "(36, 36, 7)\n"
     ]
    }
   ],
   "source": [
    "# make matrix S_t \n",
    "\n",
    "Psi_1_aux = np.expand_dims(Psi_mat, axis=1)\n",
    "Psi_2_aux = np.expand_dims(Psi_mat, axis=0)\n",
    "print(Psi_1_aux.shape, Psi_2_aux.shape)\n",
    "\n",
    "S_t_mat = np.sum(np.multiply(Psi_1_aux, Psi_2_aux), axis=2) \n",
    "\n",
    "print(S_t_mat.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# clean up some space\n",
    "del Psi_1_aux, Psi_2_aux, data_mat_swap_idx, A_2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Calculate $\\mathbf S_t$ and $\\mathbf M_t$ marix and vector\n",
    "Vector $\\vec W_t$ could be solved by\n",
    "\n",
    "$$\\vec W_t=\\mathbf S_t^{-1}\\mathbf M_t$$\n",
    "\n",
    "where $\\mathbf S_t$ and $\\mathbf M_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$S_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Psi_n\\left(X_t^k,a_t^k\\right)\\Psi_m\\left(X_t^k,a_t^k\\right)}\\quad\\quad M_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Psi_n\\left(X_t^k,a_t^k\\right)\\left(R_t\\left(X_t,a_t,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\right)}$$\n",
    "\n",
    "Define function *function_S* and *function_M* to compute the value of matrix $\\mathbf S_t$ and vector $\\mathbf M_t$.\n",
    "\n",
    "**Instructions:**\n",
    "- implement function_S_vec() which computes $S_{nm}^{\\left(t\\right)}$ matrix\n",
    "- implement function_M_vec() which computes $M_n^{\\left(t\\right)}$ column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# vectorized functions\n",
    "\n",
    "def function_S_vec(t, S_t_mat, reg_param):\n",
    "    \"\"\"\n",
    "    function_S_vec - calculate S_{nm} matrix from Eq. (75) (with a regularization!)\n",
    "    Eq. (75) in QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    num_Qbasis = 3 x num_basis, 3 because of the basis expansion (1, a_t, 0.5 a_t^2)\n",
    "    \n",
    "    Arguments:\n",
    "    t - time index, a scalar, an index into time axis of S_t_mat \n",
    "    S_t_mat - pandas.DataFrame of dimension num_Qbasis x num_Qbasis x T\n",
    "    reg_param - regularization parameter, a scalar\n",
    "    Return:\n",
    "    S_mat_reg - num_Qbasis x num_Qbasis\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 4-5 lines of code)\n",
    "    # S_mat_reg = your code goes here ...\n",
    "    num_Qbasis = S_t_mat.shape[0]\n",
    "    S_mat_reg = S_t_mat[:,:,t] + reg_param * np.eye(num_Qbasis)\n",
    "    ### END CODE HERE ###\n",
    "    return S_mat_reg\n",
    "   \n",
    "def function_M_vec(t,\n",
    "                   Q_star, \n",
    "                   R, \n",
    "                   Psi_mat_t, \n",
    "                   gamma=gamma):\n",
    "    \"\"\"\n",
    "    function_S_vec - calculate M_{nm} vector from Eq. (75) (with a regularization!)\n",
    "    Eq. (75) in QLBS Q-Learner in the Black-Scholes-Merton article\n",
    "    \n",
    "    num_Qbasis = 3 x num_basis, 3 because of the basis expansion (1, a_t, 0.5 a_t^2)\n",
    "    \n",
    "    Arguments:\n",
    "    t- time index, a scalar, an index into time axis of S_t_mat \n",
    "    Q_star - pandas.DataFrame of Q-function values of dimension N_MC x T\n",
    "    R - pandas.DataFrame of rewards of dimension N_MC x T\n",
    "    Psi_mat_t - pandas.DataFrame of dimension num_Qbasis x N_MC\n",
    "    gamma - one time-step discount factor $exp(-r \\delta t)$\n",
    "    Return:\n",
    "    M_t - np.array of dimension num_Qbasis x 1\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 2-3 lines of code)\n",
    "    # M_t = your code goes here ...\n",
    "    M_t = np.dot(Psi_mat_t, R.loc[:,t] + gamma * Q_star.loc[:, t+1])\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    return M_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([  2.22709265e-01,   2.68165972e+02,   4.46911166e+01,\n",
       "         2.00678517e+00,   1.10020457e+03,   8.44758984e-01,\n",
       "         2.29671816e+02,   2.29671816e+02,   3.78571544e-03,\n",
       "         1.41884196e-02])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "reg_param = 1e-3\n",
    "np.random.seed(42)\n",
    "S_mat_reg = function_S_vec(T-1, S_t_mat, reg_param) \n",
    "idx_row = np.random.randint(low=0, high=S_mat_reg.shape[0], size=10)\n",
    "\n",
    "np.random.seed(42)\n",
    "idx_col = np.random.randint(low=0, high=S_mat_reg.shape[1], size=10)\n",
    "\n",
    "part_3 = list(S_mat_reg[idx_row, idx_col].flatten())\n",
    "try:\n",
    "    part3 = \" \".join(map(repr, part_3))\n",
    "except TypeError:\n",
    "    part3 = repr(part_3)\n",
    "submissions[all_parts[2]]=part3\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:3],all_parts,submissions)\n",
    "\n",
    "S_mat_reg[idx_row, idx_col].flatten()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ -6.03245979e+01,  -8.79998437e+01,  -2.37497369e+02,\n",
       "        -5.62543448e+02,   2.09052583e+02,  -6.44961368e+02,\n",
       "        -2.86243249e+03,   2.77687723e+03,  -1.85728309e+03,\n",
       "        -9.40505558e+03,   9.50610806e+03,  -5.29328413e+03,\n",
       "        -1.69800964e+04,   1.61026240e+04,  -8.42698927e+03,\n",
       "        -8.46211901e+03,   6.05144701e+03,  -2.62196067e+03,\n",
       "        -2.12066484e+03,   8.42176836e+02,  -2.51624368e+02,\n",
       "        -3.01116012e+02,   2.57124667e+01,  -3.22639691e+00,\n",
       "        -5.53769815e+01,   1.67390280e+00,  -6.79562288e-02,\n",
       "        -1.61140947e+01,   1.16524075e+00,  -1.49934348e-01,\n",
       "        -9.79117274e+00,  -7.22309330e-02,  -4.70108927e-01,\n",
       "        -6.87393130e+00,  -2.10244341e+00,  -7.70293521e-01])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "Q_RL = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_RL.iloc[:,-1] = - Pi.iloc[:,-1] - risk_lambda * np.var(Pi.iloc[:,-1])\n",
    "\n",
    "Q_star = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_star.iloc[:,-1] = Q_RL.iloc[:,-1]\n",
    "\n",
    "M_t = function_M_vec(T-1, Q_star, R, Psi_mat[:,:,T-1], gamma)\n",
    "\n",
    "part_4 = list(M_t)\n",
    "try:\n",
    "    part4 = \" \".join(map(repr, part_4))\n",
    "except TypeError:\n",
    "    part4 = repr(part_4)\n",
    "submissions[all_parts[3]]=part4\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:4],all_parts,submissions)\n",
    "\n",
    "M_t\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_S* and *function_M* for $t=T-1,...,0$ together with vector $\\vec\\Psi\\left(X_t,a_t\\right)$ to compute $\\vec W_t$ and learn the Q-function $Q_t^\\star\\left(X_t,a_t\\right)=\\mathbf A_t^T\\mathbf U_W\\left(t,X_t\\right)$ implied by the input data backward recursively with terminal condition $Q_T^\\star\\left(X_T,a_T=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$.\n",
    "\n",
    "When the vector $ \\vec{W}_t $ is computed as per the above at time $ t $, \n",
    "we can convert it back to a matrix $ \\bf{W}_t $ obtained from the vector $ \\vec{W}_t $ by \n",
    "reshaping to the shape $ 3 \\times M $.\n",
    "\n",
    "We can now calculate the matrix $ {\\bf U}_t $\n",
    "at time $ t $ for the whole set of MC paths as follows (this is Eq.(65) from the paper in a matrix form):\n",
    "\n",
    "$$  \\mathbf U_{W} \\left(t,X_t \\right) = \n",
    "\\left[\\begin{matrix} \\mathbf U_W^{0,k}\\left(t,X_t \\right) \\\\  \n",
    "\\mathbf U_W^{1,k}\\left(t,X_t \\right) \\\\ \\mathbf U_W^{2,k} \\left(t,X_t \\right)\n",
    "\\end{matrix}\\right]\n",
    "= \\bf{W}_t \\Phi_t \\left(t,X_t \\right)  $$\n",
    "\n",
    "Here the matrix $ {\\bf \\Phi}_t $ has the shape shape $ M \\times N_{MC}$. \n",
    "Therefore, their dot product has dimension $ 3 \\times N_{MC}$, as it should be. \n",
    "\n",
    "Once this matrix $ {\\bf U}_t $ is computed, individual vectors $ {\\bf U}_{W}^{1}, {\\bf U}_{W}^{2}, {\\bf U}_{W}^{3} $ for all MC paths are read off as rows of this matrix.\n",
    "\n",
    "From here, we can compute the optimal action and optimal Q-function $Q^{\\star}(X_t, a_t^{\\star}) $ at the optimal action for a given step $ t $. This will be used to evaluate the $ \\max_{a_{t+1} \\in \\mathcal{A}} Q^{\\star} \\left(X_{t+1}, a_{t+1} \\right) $.\n",
    "\n",
    "\n",
    "The optimal action and optimal Q-function with the optimal action could be computed by\n",
    "\n",
    "$$a_t^\\star\\left(X_t\\right)=\\frac{\\mathbb{E}_{t} \\left[  \\Delta \\hat{S}_{t}  \\hat{\\Pi}_{t+1} + \\frac{1}{2 \\gamma \\lambda} \\Delta S_{t} \\right]}{\n",
    "  \\mathbb{E}_{t} \\left[ \\left( \\Delta \\hat{S}_{t} \\right)^2 \\right]}\\, , \n",
    "\\quad\\quad Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\mathbf U_W^{\\left(0\\right)}\\left(t,X_t\\right)+ a_t^\\star \\mathbf U_W^{\\left(2\\right)}\\left(t,X_t\\right) +\\frac{1}{2}\\left(a_t^\\star\\right)^2\\mathbf U_W^{\\left(2\\right)}\\left(t,X_t\\right)$$\n",
    "\n",
    "with terminal condition $a_T^\\star=0$ and $Q_T^\\star\\left(X_T,a_T^\\star=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$.\n",
    "\n",
    "Plots of 5 optimal action $a_t^\\star\\left(X_t\\right)$, optimal Q-function with optimal action $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ and implied Q-function $Q_t^\\star\\left(X_t,a_t\\right)$ paths are shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitted Q Iteration (FQI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/ipykernel/__main__.py:21: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "/opt/conda/lib/python3.6/site-packages/numpy/lib/function_base.py:3834: RuntimeWarning: Invalid value encountered in percentile\n",
      "  RuntimeWarning)\n",
      "/opt/conda/lib/python3.6/site-packages/ipykernel/__main__.py:77: RuntimeWarning: invalid value encountered in less\n",
      "/opt/conda/lib/python3.6/site-packages/ipykernel/__main__.py:78: RuntimeWarning: invalid value encountered in greater\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Time Cost: 0.2872748374938965 seconds\n"
     ]
    }
   ],
   "source": [
    "starttime = time.time()\n",
    "\n",
    "# implied Q-function by input data (using the first form in Eq.(68))\n",
    "Q_RL = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_RL.iloc[:,-1] = - Pi.iloc[:,-1] - risk_lambda * np.var(Pi.iloc[:,-1])\n",
    "\n",
    "# optimal action\n",
    "a_opt = np.zeros((N_MC,T+1))\n",
    "a_star = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_star.iloc[:,-1] = 0\n",
    "\n",
    "# optimal Q-function with optimal action\n",
    "Q_star = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_star.iloc[:,-1] = Q_RL.iloc[:,-1]\n",
    "\n",
    "# max_Q_star_next = Q_star.iloc[:,-1].values \n",
    "max_Q_star = np.zeros((N_MC,T+1))\n",
    "max_Q_star[:,-1] = Q_RL.iloc[:,-1].values\n",
    "\n",
    "num_basis = data_mat_t.shape[2]\n",
    "\n",
    "reg_param = 1e-3\n",
    "hyper_param =  1e-1\n",
    "\n",
    "# The backward loop\n",
    "for t in range(T-1, -1, -1):\n",
    "    \n",
    "    # calculate vector W_t\n",
    "    S_mat_reg = function_S_vec(t,S_t_mat,reg_param) \n",
    "    M_t = function_M_vec(t,Q_star, R, Psi_mat[:,:,t], gamma)\n",
    "    W_t = np.dot(np.linalg.inv(S_mat_reg),M_t)  # this is an 1D array of dimension 3M\n",
    "    \n",
    "    # reshape to a matrix W_mat  \n",
    "    W_mat = W_t.reshape((3, num_basis), order='F')  # shape 3 x M \n",
    "        \n",
    "    # make matrix Phi_mat\n",
    "    Phi_mat = data_mat_t[t,:,:].T  # dimension M x N_MC\n",
    "\n",
    "    # compute matrix U_mat of dimension N_MC x 3 \n",
    "    U_mat = np.dot(W_mat, Phi_mat)\n",
    "    \n",
    "    # compute vectors U_W^0,U_W^1,U_W^2 as rows of matrix U_mat  \n",
    "    U_W_0 = U_mat[0,:]\n",
    "    U_W_1 = U_mat[1,:]\n",
    "    U_W_2 = U_mat[2,:]\n",
    "\n",
    "    # IMPORTANT!!! Instead, use hedges computed as in DP approach:\n",
    "    # in this way, errors of function approximation do not back-propagate. \n",
    "    # This provides a stable solution, unlike\n",
    "    # the first method that leads to a diverging solution \n",
    "    A_mat = function_A_vec(t, delta_S_hat, data_mat_t, reg_param)\n",
    "    B_vec = function_B_vec(t, Pi_hat, delta_S_hat, S, data_mat_t)\n",
    "    # print ('t =  A_mat.shape = B_vec.shape = ', t, A_mat.shape, B_vec.shape)\n",
    "    phi = np.dot(np.linalg.inv(A_mat), B_vec)\n",
    "    \n",
    "    a_opt[:,t] = np.dot(data_mat_t[t,:,:],phi)\n",
    "    a_star.loc[:,t] = a_opt[:,t] \n",
    "\n",
    "    max_Q_star[:,t] = U_W_0 + a_opt[:,t] * U_W_1 + 0.5 * (a_opt[:,t]**2) * U_W_2       \n",
    "    \n",
    "    # update dataframes     \n",
    "    Q_star.loc[:,t] = max_Q_star[:,t]\n",
    "    \n",
    "    # update the Q_RL solution given by a dot product of two matrices W_t Psi_t\n",
    "    Psi_t = Psi_mat[:,:,t].T  # dimension N_MC x 3M  \n",
    "    Q_RL.loc[:,t] = np.dot(Psi_t, W_t)\n",
    "    \n",
    "    # trim outliers for Q_RL\n",
    "    up_percentile_Q_RL =  95 # 95\n",
    "    low_percentile_Q_RL = 5 # 5\n",
    "    \n",
    "    low_perc_Q_RL, up_perc_Q_RL = np.percentile(Q_RL.loc[:,t],[low_percentile_Q_RL,up_percentile_Q_RL])\n",
    "    \n",
    "    # print('t = %s low_perc_Q_RL = %s up_perc_Q_RL = %s' % (t, low_perc_Q_RL, up_perc_Q_RL))\n",
    "    \n",
    "    # trim outliers in values of max_Q_star:\n",
    "    flag_lower = Q_RL.loc[:,t].values < low_perc_Q_RL\n",
    "    flag_upper = Q_RL.loc[:,t].values > up_perc_Q_RL\n",
    "    Q_RL.loc[flag_lower,t] = low_perc_Q_RL\n",
    "    Q_RL.loc[flag_upper,t] = up_perc_Q_RL\n",
    "    \n",
    "endtime = time.time()\n",
    "print('\\nTime Cost:', endtime - starttime, 'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k8niGSzfmefXqAqtTK6RLBgNlg5TjZoSI36DrVJxT59tIj6XoGoph6hoKh5b9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RW88RBBczl6rISvtVYJWqsEwSpBox4NPI6Egw5v0PQm7k0CWtEj+s8cN8fHMXEshg9rDwo8R86N\nHDmMPDnLk2MHOVuKViniA5IyuXwZy1fI5Srk8lVyhfBhhRq5wg5yxR3h66npkv7j+IqHmXadE5Hp\npcA+jTaw1WMu+po/rmtyx7zVY/TVixWCYoWgWCIolPBiiaBQJCgUCPIFPF8gyOejR44glyPIgRsE\nOQsHCdHgxNuDk8TqRiNxHARrtDrn1AmCh/DWGkEzOdgZH4sF+iGrFql1GsWBaZbwtWJ/3UZPfUfq\nQMSKGmyICKDAvjHjuINQX8BOuyb3OPL5fcvKsaCb8VaPBuSjx7RwDwiCRt/qRnIlY1iapR5Ll8RS\nMikplPbAY3rqNgYUfg4ZdCTrNmKDjrS6jc5r7YHHnNRtiMwoBfbvXgd3fGa0SubMtnrcaF63qq0e\n12GWI58vA+VJN6Wjt26jO8hI1mAkBx71vu/pH2Q0Bg46mq1lPLVuo/v8uAoEB4gXa6ZdcdI78Bi8\n2lFOrFikFYimDzzKfQMPs2kacoqMnwL7fd+DOz/fHyi11aNssVmq20hd3UhZ7Qi8kVowmrpq0Tlv\nlWbzaPpqSTTo8OPZynUAs3xqgWhi4DHwqpT+QUd31SJl4DFS3UaJXE5/imV89K/poteGDxEBiIJM\ngXx+cveT7uXe6hZ+dgYU9b4BRO8VJ+kDj/66je7AozuwaDWW+8/puTJmfHKxFYVhV6UMG3gU1xl4\nDF7tSNZ3qG5j1k00sJvZFcAfAL+IXvpzd//05FokItPILE8+XyWfr066KR3Juo16ysCjf+UiOfCo\np6xuNAbUbUSplCF1G+3VjXHqG2gMLQ4dtgdHvL6j3F+nsc5qR7wdGmysbxpm7G9z97dOuhEiIhuR\nrNtYmHRzgGF1GwPqL9orH/GBx5D9NdL24Gi2HsYbD6QOMra6bmP0/TXS0izlAQOPtEFFfOBR7l8B\nmbIi0WkI7CIiMgbTWLcRDjaaA6848cQAozHiaseggUd/3UZamiWLuo2dO8/lcY+9cmw/YyOmIbC/\nysxeDBwG/sTdH5h0g0REZDzCwUa4idQ06dZtxOsn0uo2hq129JwXG3SUy/sm9ruZ+/iWSFJ/gNkN\nQNpveDlwI3Af4TrNG4GT3f2lAz7nMuAygAMHDjzhnnvu2ZoGi4iITBkz+5a7Hxrp3K0O7KMys4PA\np9z9/PXOPXTokB8+fHjL2yQiIjINNhLYJ5rxN7OTY4eXALdOqi0iIiLzYNI59r83swsIl+LvBv5w\nss0RERGZbRMN7O7+okn+fBERkXkzXRffiYiIyKYosIuIiMwRBXYREZE5osAuIiIyRyZdFS8iIjIX\ngsBZW2myttIkaDm79k7mDokK7CIiIoT72jfqLerLYXCuLzeoLzeprzTDr8tN1pab1FcaneP6Svu1\nJmurzc79bk46bSe/e/mFE/k9FNhFRGQuuDutRpAIxPXlRhSk44G4kTwnFpw9GL4ba7Gcp1wrUK4V\nKFULLJxQoXxqdFwrUK6Gz3fuqmT0W/dTYBcRkanRagVhkO0E3UZsBt0TnOOz6WiGHTSHB+Z8MdcJ\nvuVagepCiV17a+FxNR6ci4kAXqkVKVXz5PLTX5qmwC4iImMTzzO3Z8yJpeyVnoCdWOpu0FwLhn5+\nLmdh8I3PjndXKO/oHrcDc3wGXY4Cc6GYz6gnJkeBXUREOjadZ15pDv8BRifYlqKvux5R61vKLteK\nqTPoQimHmWXTGTNKgV1EZI5MLM+8f8BSdvu19qy5nMdyCsxbSYFdRGTKZJJnjs2O0/LMYU65m4sO\n35udPPN2psAuIjJmWeSZyzuipewo+C6cUFlnKXt75Zm3MwV2EZEe8TxzGIhjM+OH48vWKXnm5QZr\nq63hPyAtz7y3tv5SdlV5ZlmfAruIzJ1M8syVfCI49+aZE0vZ1UJ3hq08s2wxBXYRmUpbnWcuFHOJ\nZeraYjLP3J4xK88ss0aBXUS2ROZ55h3F4Xnm+PXNyjPLHFNgF5FU2eeZi4k8c6VWoFQtEq/eLinP\nLLIuBXaROZXIMz/cXaIedSl7baW1oTxzuVZM5Jm7VdjJpWzlmUW2lgK7yBRrNYOeQNxIWcqOAnHP\nUnZ9pbnBPHMxmWeOzY5LUfFXd8tO5ZlFppUCu8gWyjTPHBV7tfPMldjsOLmU3X0tX1RgFpk3Cuwi\nQ2SZZ24vW7fzzN2l62JsBh3LM+8oUCgqzywiSQrsMtc2nWdebuLDV7NjeebujLm8v7cKuz/PXKkV\nKSrPLCJjlklgN7PnA1cA5wEXuvvh2HtvAF4GtIBXu/vnsmiTzI7M8szR8nQ7z1zpqcJOu/tUqaI8\ns4hMl6xm7LcCzwPeG3/RzB4N/B7wGOAU4AYze5S7r7N+KbOknWdO3AYyLc8cvd4Jzg+Hx6PmmeMz\n44UTKn1V2MmlbOWZRWQ+ZRLY3f12IC0X+FzgI+5eB35gZncCFwJfy6JdMpqBeeaUnHLaUvZ6eWYz\nYkvVsTxz/PrllDxzpVakVFOeWUQkbtI59lOBG2PH90av9TGzy4DLAA4cOLD1LZsjmeWZY8vWCydU\n2LN/Z98NLZK55nDGrDyziMj4jC2wm9kNwL6Uty5392s3+/nufiVwJcChQ4fWCTPzJ4s8c5hD7uaZ\nd++r9VVhp919SnlmEZHpMbbA7u7PPI5v+zFwWux4f/Ta3NnyPHPe+nb6Wjix0rdlZ99SdrTPtvLM\nIiLzYdJL8Z8EPmxm/0BYPHc28I3JNildJnnmnsujdu+t9Vdhx28D2Z4xK88sIiKRrC53uwR4B7AH\nuM7MbnL3Z7n7d8zso8BtQBN4ZdYV8T+/5yj/94Oj6y5lj5JnLlXyicujFk+sUB6aZ+7OoJVnFhGR\ncciqKv4a4JoB770JeFMW7Ujzg5vv4/B1dwNQKOWiZeooz7zUk2cetJStPLOIiEyJSS/FT9wFzziN\nX3nqfuWZRURkLmz7wF6uFSfdBBERkbHZ9oFdRERks+rNFkdWGhxdaXBkpYGZ8fgDuyfSFgV2ERER\noNkKOBIF5r7HcoMHU15rP19pJOu+zzt5kc+85jcm8nsosIuIyNxoBc6x1W7AfXA5PUh33o/Nsh+q\nN4d+drWYZ6laZFetyGK1yIETa+FxtchStchSLfpaLbJnoZzRb9xPgV1ERKaKu3Os3kwE4PijHayP\ndoLzWidgH6sPvzS5VMglgvEpSxXO27eQCMrt4N09LrFYLVAu5LPrhE1QYBcRkbFzd5bXWusH45Vm\nFJTXOuceXW3SCgZH50LOOrPmpWqRk3aWeeSenZ1AvFgtsqtWSg3UleJsBOfNUGAXEZGBVhv9wbm7\npL2WnEmvJIN3ozU4OOeMROANl7Z3sFQtdINxtdQJ3vHgXCvltdPmEArsIiJzbq0ZLwqLBePegrCe\nwP3gSoO15vD7VCxWColl7FOWqqnBOPGoFdlZKpDTbptbQoFdRGQGNFsBR1eb0cw5tmzdM5PunTU/\nuNxfsd1rZ7nQmTUvVQuc1V7WTgnK8UC9UCmSV3CeOgrsIiIZCQLnWDs4x2bOffnnlKKxUSu22wH5\ntBNqnN9Z0u4G6cV4FXd0XNR22HNFgV1EZAPcnYfqzU4APtozUx64rL28NnLFdjsYn7xU4dx9C1Ex\nWPrMub3sPSsV27L1FNhFZNtxd1YarZRisP4cc3LJe22kiu34zPnEnSXO3LOjM0te7ATm/qrt7VCx\nLVtPgV1EZla8YjutGKwdjNM2I1mvYju+ZL1YLXLa7mpKIVgpEcR3qWJbpoACu4hMVLJiOwrGK2vR\n7LnZyUWn5Z/r61RsL1QKiWC8b6mSDMZpVduq2JYZp8AuIpsWr9iO55SHFYO1H8trwyu2d5Ty7KqV\nOhXb4bJ2aWAxWDtQq2JbtisFdhEBkhXbvVXb6cVg3Rn2sY1UbFeTFdtphWDxJXBVbItsjAK7yByJ\nV2yPVgwWO15tDK/YzucS1zXHK7bTlrTjW36qYlskOwrsIlOmXbGdto1nbzDuLQg7stIYuWJ7sdqt\n2O7bGSylartSzKkoTGQGKLCLbJHVRit5jfOAW0UmdxJrcmRlbaSK7cTS9u7qgO07S4kdxHaoYltk\n7imwiwzRaAWJmXMyGPcWgiV3EhulYjsejMOK7Z5LqHqC9WK1yEJZFdsiMpgCu8y9VuBDdgfr39az\ne8nVaBXb4Yy4xFK1wBkn7UgsY/cWg7UDtSq2RWSrZBLYzez5wBXAecCF7n44ev0gcDtwR3Tqje7+\n8izaJLMlCJxj9eaAHHP3Oue0ncTWq9iuFHOdW0QuVYvs311j16mDC8HagVoV2yIyjbKasd8KPA94\nb8p733f3CzJqh0yQu/PwWiuRUx6lGOzB5QbHVhsMqQnrq9jeu1jhnL0Lw28fWVPFtojMn0wCu7vf\nDqhoZw64O6uNoHuN8/LgYNy7rH10pUFzSHTO5yxx/fLuWqmztJ36qHVn2arYFhEJTUOO/Qwzuwk4\nAvyFu39p0g3aDurN1sANRwY92sVja63BRWFm9AXg/VHFdtpmJPEdxFSxLSKyeWML7GZ2A7Av5a3L\n3f3aAd/2U+CAu//SzJ4AfMLMHuPuR1M+/zLgMoADBw6Mq9kzLV6xPcruYPF89GpjtIrtdiDeu7gz\nGYwHBGpVbIuITNbYAru7P/M4vqcO1KPn3zKz7wOPAg6nnHslcCXAoUOHhmRbZ0u8Yrt3d7DuPttr\nfbPmIysNHh6xYrt9L+eDJ9VYqi51qrZ7i8Hil1SpYltEZDZNdCnezPYA97t7y8zOBM4G7ppkm45H\nvGJ71Guc28+PrY5Wsd2u2t6/u8bSKSnFYH0bk6hiW0RkO8rqcrdLgHcAe4DrzOwmd38W8BTgb8ys\nAQTAy939/iza1CtesR3e03ltnUCdLA5br2K7fWeqXbUSexcrPGrvQsoWnsnjxWqRSlEV2yIiMrqs\nquKvAa5Jef1q4Oos2jDIe77wfd73xbs4MkLFdvz65d21EgdP3NG3K9iunhn0rmpJFdsiIpKZaaiK\nn6gzT9rBs8/fN3AzkvYOYqrYFhGRWbDtA/vFj9nHxY9JK+YXERGZPaquEhERmSMK7CIiInNEgV1E\nRGSOmPvs7fViZr8A7hnjR54E3DfGz9uO1IfjoX7cPPXh5qkPN2/cfXi6u+8Z5cSZDOzjZmaH3f3Q\npNsxy9SH46F+3Dz14eapDzdvkn2opXgREZE5osAuIiIyRxTYQ1dOugFzQH04HurHzVMfbp76cPMm\n1ofKsYuIiMwRzdhFRETmyLYK7GZ2t5ndYmY3mVnfPd8t9E9mdqeZ3Wxmj59EO6fZCH34wqjvbjGz\nr5rZ4ybRzmm2Xh/GzvtVM2ua2aVZtm9WjNKPZva06P3vmNkXsm7jtBvh/+clM/sPM/ufqA9fMol2\nTjMz22VmHzOz75rZ7Wb2pJ73M48r23Gv+Ke7+6BrC59DeE/4s4FfA94dfZWkYX34A+Cp7v6AmT2H\nMM+kPuw3rA8xszzwd8D12TVpJg3sRzPbBbwLeLa7/9DMHpFt02bGsH+LrwRuc/ffNrM9wB1m9iF3\nX8uwfdPu7cBn3f1SMysBtZ73M48r22rGPoLnAv/moRuBXWZ28qQbNUvc/avu/kB0eCOwf5LtmWGv\nIryl8c8n3ZAZ9gLg4+7+QwB3V19unAMLFt7acidwP9CcbJOmh5ktAU8B3g/g7mvu/mDPaZnHle0W\n2B24wcy+ZWaXpbx/KvCj2PG90WvStV4fxr0M+EwGbZo1Q/vQzE4FLiEc2ctg6/1bfBSw28z+Kzrn\nxRm3bxas14fvBM4DfgLcArzG3YMsGzjlzgB+AXzQzL5tZleZ2Y6eczKPK9ttKf4id/9xtCT3n2b2\nXXf/4qQbNWNG6kMzezphYL8o8xZOv/X68B+BP3X3IJwoyQDr9WMBeALwDKAKfM3MbnT3/51EY6fU\nen34LOAm4DeBs6JzvuTuRyfR2ClUAB4PvMrdv25mbwf+DPjLSTZqW83Y3f3H0defA9cAF/ac8mPg\ntNjx/ug1iYzQh5jZY4GrgOe6+y+zbeH0G6EPDwEfMbO7gUuBd5nZ72TayBkwQpgTW3sAAAP5SURB\nVD/eC3zO3R+OcshfBFTMGTNCH76EMJ3h7n4nYQ3Nudm2cqrdC9zr7l+Pjj9GGOjjMo8r2yawm9kO\nM1toPwcuBm7tOe2TwIujKsYnAkfc/acZN3VqjdKHZnYA+DjwIs2M+o3Sh+5+hrsfdPeDhH8oXuHu\nn8i8sVNsxP+frwUuMrOCmdUIC5Zuz7al02vEPvwh4YoHZrYXOAe4K8t2TjN3/xnwIzM7J3rpGcBt\nPadlHle201L8XuCaaGmzAHzY3T9rZi8HcPf3AJ8Gfgu4E1gmHK1K1yh9+FfAiYSzTICmbiaRMEof\nyvrW7Ud3v93MPgvcDATAVe7eG7i2s1H+Lb4R+BczuwUwwhSR7vqW9CrgQ1FF/F3ASyYdV7TznIiI\nyBzZNkvxIiIi24ECu4iIyBxRYBcREZkjCuwiIiJzRIFdRERkjmyny91E5o6ZnQh8PjrcB7QIt7gE\nWHb3Xx/zz6sB7wMeS3j504PAswn/lrzA3d81zp8nIhuny91E5oSZXQE85O5v3cKf8QZgj7u/Ljo+\nB7gbOBn4lLufv1U/W0RGo6V4kTllZg9FX59mZl8ws2vN7C4ze7OZvdDMvhHdi/us6Lw9Zna1mX0z\nejw55WNPJrYdprvf4e514M3AWRbe1/st0ee9Pvqcm83sr6PXDlp43+oPWXjv6o9FqwBE7botOn/L\nBici805L8SLbw+MI79J1P+HuWFe5+4Vm9hrCnbNeS3hf6be5+5ejrYE/F31P3AeA683sUsIUwL+6\n+/cIb3xxvrtfAGBmFxPef/pCwiX7T5rZUwi3KD0HeJm7f8XMPgC8wsw+SHhHu3Pd3S28l7qIHAfN\n2EW2h2+6+0+j2fX3geuj128BDkbPnwm808xuItzfetHMdsY/xN1vAs4E3gKcAHzTzHqDP4T7jl8M\nfBv4b8Ibh5wdvfcjd/9K9PzfCe8AeARYBd5vZs8j3HpTRI6DZuwi20M99jyIHQd0/w7kgCe6++qw\nD3L3hwhv9PNxMwsI98G+uuc0A/7W3d+beNHsIOE9wHs+0ptmdiHhTTQuBf6I8FahIrJBmrGLSNv1\nhMvyAJjZBb0nmNmTzWx39LwEPBq4BzgGLMRO/Rzw0vaM38xOje75DXDAzJ4UPX8B8OXovCV3/zTw\nx+j2qiLHTTN2EWl7NfDPZnYz4d+GLwIv7znnLODdFt4SLAdcB1wd5cW/Yma3Ap9x99dHS/Rfi+4e\n9hDw+4SX490BvDLKr98GvBtYAq41swrhbP91W/y7iswtXe4mIpmJluJ1WZzIFtJSvIiIyBzRjF1E\nRGSOaMYuIiIyRxTYRURE5ogCu4iIyBxRYBcREZkjCuwiIiJzRIFdRERkjvw/jYsBmrRj3jsAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0681d0e208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot both simulations\n",
    "f, axarr = plt.subplots(3, 1)\n",
    "f.subplots_adjust(hspace=.5)\n",
    "f.set_figheight(8.0)\n",
    "f.set_figwidth(8.0)\n",
    "\n",
    "step_size = N_MC // 10\n",
    "idx_plot = np.arange(step_size, N_MC, step_size)\n",
    "axarr[0].plot(a_star.T.iloc[:, idx_plot]) \n",
    "axarr[0].set_xlabel('Time Steps')\n",
    "axarr[0].set_title(r'Optimal action $a_t^{\\star}$')\n",
    "\n",
    "axarr[1].plot(Q_RL.T.iloc[:, idx_plot]) \n",
    "axarr[1].set_xlabel('Time Steps')\n",
    "axarr[1].set_title(r'Q-function $Q_t^{\\star} (X_t, a_t)$')\n",
    "\n",
    "axarr[2].plot(Q_star.T.iloc[:, idx_plot]) \n",
    "axarr[2].set_xlabel('Time Steps')\n",
    "axarr[2].set_title(r'Optimal Q-function $Q_t^{\\star} (X_t, a_t^{\\star})$') \n",
    "\n",
    "plt.savefig('QLBS_FQI_off_policy_summary_ATM_eta_%d.png' % (100 * eta), dpi=600)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the optimal action $a_t^\\star\\left(X_t\\right)$ and optimal Q-function with optimal action $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ given by Dynamic Programming and Reinforcement Learning.\n",
    "\n",
    "Plots of 1 path comparisons are given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KjQd5s/AYdU0tGgD6whir+2fWxRD5eann9Xb+f66P5P/B9RTQK8BtwIP2/9Ud\nJzDG/Bj4MYB9BPCDwd74t7UZDlefbk/VOOfnT9Q3t08XGRpM1vBocjKGkZuU1p66GZ0Q7dWXdEeG\nBXNTTjo3ZlvpoafWf54eWjJ5JLefr+khdabTTa384b0iQoOFdXsrOFRVT1p8lKeb5RsOfwInD8LF\nPz5jcH5RJUmx4WQlRXuoYX3nagB4EHhORL4GHABuBBCRZODPxpgrXJx/n7W0tvGvHcfP6HFTXFFL\nQ/Pn3Srjo8MYmxTDZVNHWXvySdZJ2eS4SJ/J3XWmq/TQm4VWeuj2eVZ6KDJM00OB7ukNByivaeTR\nm2dyz6otPLvpED+49Kz+G6ozO+z0z4TPN2/GGNYXVXL+2ASf2tFyqRfQQOtPLyBjDFPvf4u6plZS\nhkae0dMmy07dxEeHDVCLvU9Ds9V76MmPPu89dFNOGrfOGU3qMN3jC0R1jS1c+Mt3mZw8hL9/bTZf\n/esmCo+c5KMfXeITFy95lDHwyDkwfDJ86bn2wXuP17D44Q/43+vP4aYcz3ZeGcxeQF5HRFh99wUk\nD40gKszvVq/PIkI/Tw9t3F/FX9eX8PgHxTz+QTFLJlu9h+ZkanookDyVX0JlXRP3Lh4PwE05aXzz\n72W8t7ucRZO76sinADi8GU4egovP6ANDvg/V/3Hml1vIscNjPN0EryMizM5MYHZmAoerT/P0hgPt\nJwE1PRQ4ahqaWfFBMZdMHM7MdOsE5iUTh5MUG86qTQc1APSkMA+Cw2DC5WcMXr+vkpShkT53HkWP\n9wJQytBIfnTZRDb8eCH/e/05iAjLX9rGnP9Zy/+8sZPSE/WebqIaIE9+VEJ1fTPfWzS+fVhocBA3\nnJfKO7vKOHaywYOt83JtbXbvn4UQOdRpsCG/uJJ5PlD+uSMNAAHMkR56/TsX8Owdczh/bAJ/Xref\nC3/5Lt/8ewH5RZV48zki1TcnTzfz+LpiFk8ewTmpcWeMuyknjTYDL2w+5KHW+YDDBXCq9Iw7fwHs\nOHqKk6ebmTfW9wKAX6aAVN90lh5atfEgbxUeZ+LIWG6bl8G1mh7yeX9ZV0xNQ8sZe/8OoxOimZeV\nwLMFh7hrwVif7g03YArzIDj8rPSPo/7/3Ezfyv+DHgGoDhzpofwfL+SX109DRPixIz30+k4OVWl6\nyBedqGviiY9KuOKckUzuok597qx0DlWd5qOiikFunQ9wpH/GLoKIM9+/9UWVZCZGMzIuwkON6z8N\nAKpTEaEhMikCAAAgAElEQVTB3JiTxuvfuYDnvjnXSg99uJ+LfmWlh9YXVWh6yIesWFdMXVML93Sy\n9++wZPIIhkaFsmqTpoHOUroRao6clf5paW1j4/4qn7j9Y2c0BaS6JSLMGhPPrDHxHHHqPfRW4XEm\njIjl9vM1PeTtKmobeWp9CVdPS2b8iK7rMUaEBnPdzFT+vqGEytpGEmLCB7GVXq7wZTv9c9kZg7cd\nPkltY4vPBgA9AlC9ljw0kh860kNfmEZQkKaHfMGf3i+iobmV7y4a1+O0ubPSaG41vPTJ4UFomY9o\na4MdL8O4xRB+ZgB11P+Z46O1lDQAqD6LCA3mxuzO00N3/E3TQ96k7FQDf8s/wLUzU8hK6vn6mPEj\nYjk3fSirNh3Uz9Dh0MdQc/Ss9A9Y9X8mjowl0UePljQFpPqtq/TQv3ZY6aHb5mWwbKamhzzpD+8V\n0dJm+O7Cnvf+HXJnpfPDFz6j4MAJcjLiB7B1PqIwD0IiYPylZwxubGml4EAVuR4u/eAKPQJQbtEx\nPRQcJPxHnpUe+m9ND3nE0ZOn+cfGg3zh3FRGJ/S+QuVV00YREx7Cyo0HB7B1PqKtFXas7jT9s/Vg\nNQ3NbT55AZiDBgDlVo700GvfuYDn75zLBWMT+YudHrr32a20tmlaYbA89u4+jDHcfcnYPr0uKiyE\na2Yk8/q2o5w83dzzC/zZwQ1Qe6zT9M/6okqCBJ++l4IGADUgRIScjHge+9K5rPvhxdw2L4OXthzm\nmY8PeLppAaH0RD3PbjrEjdlp/apPc3NOOg3NbbyyNcBPBhfmQUgkjLv0rFH5xZVMTYkjLjLUAw1z\nDw0AasAlD43kv66azPxxifzqzd2UndJ6MwPt9+/sQ5A+7/07nJMax5TkIazceChwTwY70j/jl0D4\nmSfQTze1suXgCeb68N4/aABQg0RE+NnSqTS2tvGL13Z6ujl+7UBlHc9vLuWLs9MZFdf/W4Lm5qSx\n4+gpth8+5cbW+ZAD66GurNP0T8GBKppbjc/2/3fQAKAGzZjEaO5akMUrnx5h3d5yTzfHbz26dh8h\nQcJdC7Jcms/SmSlEhAaxclOAngze8bKd/lly1qj1RZWEBInP95LSAKAG1Z0XZZGREMV/rS6kobnV\n083xO8XlteRtKeXWOaMZPsS12jRDIkK58pxkXtl6hLrGFje10Ee0p38uhbCze1DlF1UyPW0o0eG+\n3ZNeA4AaVBGhwfz82qnsr6jj/94v8nRz/M6ja/cSHhLMnS7u/TvkzkqjtrGF17Yddcv8fMaBj6Cu\nvNP0z6mGZj4rrfbp7p8OGgDUoJs/Lomrpyfzh/eK2F9R5+nm+I29x2tY/ekRbpuX4bYrU7NHD2Ps\n8BhWBdo1AYV5EBrVafpn0/4q2gw+n/8HDQDKQ+67chLhwUH81+rtgdvLxM0eWbuXqNBg7rgw023z\nFBFyc9L45GA1e47XuG2+Xq21BXa8AuMvg7Czu9DmF1USFhLEufYtNX2ZBgDlEcOHRPCDSyewbm8F\n//wswNILA2Dn0VO89tlRvnrBGOKjw9w67+vOTSU0WFi1MUDKRB/4EOorOk3/gHUC+Lz0YUSE+n6J\nEw0AymNumTOac1Li+PmrOzjVEOBXnLrokbf3EBsRwtcvcN/ev0N8dBhLpozkpS2lgXHivjAPQqOt\n8g8dnKhrYsfRU36R/wcNAMqDgoOE/7dsKhW1jfzmrd2ebo7P2n74JG8VHufrF2QSFzUwV6XenJNO\ndX0zbxUeG5D5ew1H+mfC5RB69jUUH++3yj/74v1/O+NSABCReBFZIyJ77f+dJsVEZKiIvCAiu0Rk\np4jMdWW5yn9MSx3Kl+eM5u8bDvBZabWnm+OTHl6zh7jIUL5yQcaALWNeVgJp8ZH+nwYq+QBOV3Wb\n/okKC2Za6tBBbtjAcPUIYDmw1hgzDlhrP+/Mb4E3jTETgemAXgqq2n3/0gkkxITzk7ztWiyuj7Yc\nPMHaXWXccWEmQyIGriZNUJBwU3Ya+cWVlPhzz63ClyEsBsYu7HT0+qJKcjLiCQ32j+SJq2uxFHjK\nfvwUcG3HCUQkDrgQ+AuAMabJGKO7eqrdkIhQ7rtqMtsOn9RicX308Nt7iY8O4/Z5GQO+rBuy0wgO\nEp4t8NOjgNZm2PnPLtM/Zaca2FdW6zf5f3A9AIwwxji6cBwDRnQyzRigHHhSRLaIyJ9FpMvi5CJy\nh4gUiEhBebmWCwgUV08bxQVjtVhcXxSUVPHBnnLuvChzUK5IHTEkgosnDOf5glKaW9sGfHmDbn/3\n6Z/8Yiv/7w/9/x16DAAi8raIbO/kb6nzdMbqzN3Z8XsIcC7wR2PMTKCOrlNFGGNWGGOyjTHZSUlJ\nfVsb5bNEhJ9fq8Xi+uKhNXtIjAnn1jkZg7bM3Jw0KmobeWdX2aAtc9AU5kFYLGR1nv7JL6okNiKE\nKclxg9ywgdNjADDGLDLGTO3kbzVwXERGAdj/O/tWlAKlxpiP7ecvYAUEpc4wJjGab12kxeJ6I7+o\nkvVFldy1IGtQb7m5YEISI4aE+9+VwY70z8QrILTzGkrriyqZk5lAcJAMcuMGjqspoFeA2+zHtwGr\nO05gjDkGHBKRCfaghcAOF5er/NS3FmixuJ4YY3h4zR5GDAnni7MH9360IcFB3Jidxvt7yjlSfXpQ\nlz2git+Hhuou0z+lJ+o5WFXv8/X/O3I1ADwILBaRvcAi+zkikiwirztN923gGRH5DJgB/LeLy1V+\nSovF9ezDfRVsLKni7ovHeuRq1Buz02gz8HxB6aAve8AU5kH4EMi6pNPR+UX+1f/fwaUAYIypNMYs\nNMaMs1NFVfbwI8aYK5ym22rn9acZY641xpxwteHKf2mxuK4ZY3hozR6S4yK4MSfNI21Ii49i/rhE\nnis45B/ddluaYNc/YeKVENJ5Eb38okoSosMYPzy20/G+yj86syq/o8XiOvfe7nK2HKzm7kvGER7i\nuVo0uTnpHK4+7R/naorfg4aTXaZ/jDHkF1v5/yA/yv+DBgDlpZyLxb2qxeKAz/f+0+IjuSE71aNt\nWTR5OPHRYTy7yQ+uCdjxMoTHQebFnY4uqazn6MkGv+r+6aABQHktR7G4n2mxOADW7DjOtsMn+fYl\n4zx+JWp4SDDXn5vCmh3HKa9p9GhbXNLSBDtftdM/nVdRXV9UAeBXF4A5aABQXsu5WNxD/9rj6eZ4\nVFub4eG395KREMV1M1M83RwAbspJp6XN8OInPnwyuPhdaOw6/QNW98+RQyIYk9jl9as+SwOA8mqO\nYnF/yy9hW+lJTzfHY94sPMbOo6f47qJxhHhJHZqxw2PIyRjGs5sO+e55msI8iIiDzAWdjjbGsKGo\nkrlZCYj4V/4fNAAoH9BeLO7lbf7R66SPWtusfv9ZSdFcM9079v4dcnPS2V9Rx8f7qzzdlL5raYRd\nr8HEq7tM/+w5XktlXZNf5v9BA4DyAY5icZ+VBmaxuNe2HWVvWS33LBrvdVehXnHOKGIjQnzzyuCi\nd6DxVA/pH//N/4MGAOUjArVYXEtrG4+8vYcJI2K58pxRnm7OWSLDgrl2Rgqvbz/GyXofO1FfmAcR\nQyHzoi4nyS+qJC0+ktRhZ98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oMK9++wIECeh7yQ608JBgrjs3lb/ll1BZ20hCTP8Lt1XX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0680580e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot a and a_star\n",
    "# plot 1 path\n",
    "\n",
    "num_path =  120 # 240 # 260 #  300 # 430 #  510\n",
    "\n",
    "# Note that a from the DP method and a_star from the RL method are now identical by construction\n",
    "plt.plot(a.T.iloc[:,num_path], label=\"DP Action\")\n",
    "plt.plot(a_star.T.iloc[:,num_path], label=\"RL Action\")\n",
    "plt.legend()\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Optimal Action Comparison Between DP and RL')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary of the RL-based pricing with QLBS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "       QLBS RL Option Pricing       \n",
      "---------------------------------\n",
      "\n",
      "Initial Stock Price:      100\n",
      "Drift of Stock:           0.05\n",
      "Volatility of Stock:      0.15\n",
      "Risk-free Rate:           0.03\n",
      "Risk aversion parameter : 0.001\n",
      "Strike:                   100\n",
      "Maturity:                 1\n",
      "\n",
      "The QLBS Put Price 1 :    nan\n",
      "\n",
      "Black-Sholes Put Price:   4.5296\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# QLBS option price\n",
    "C_QLBS = - Q_star.copy() # Q_RL # \n",
    "\n",
    "print('---------------------------------')\n",
    "print('       QLBS RL Option Pricing       ')\n",
    "print('---------------------------------\\n')\n",
    "print('%-25s' % ('Initial Stock Price:'), S0)\n",
    "print('%-25s' % ('Drift of Stock:'), mu)\n",
    "print('%-25s' % ('Volatility of Stock:'), sigma)\n",
    "print('%-25s' % ('Risk-free Rate:'), r)\n",
    "print('%-25s' % ('Risk aversion parameter :'), risk_lambda)\n",
    "print('%-25s' % ('Strike:'), K)\n",
    "print('%-25s' % ('Maturity:'), M)\n",
    "print('%-26s %.4f' % ('\\nThe QLBS Put Price 1 :', (np.mean(C_QLBS.iloc[:,0]))))\n",
    "print('%-26s %.4f' % ('\\nBlack-Sholes Put Price:', bs_put(0)))\n",
    "print('\\n')\n",
    "\n",
    "# # plot one path\n",
    "# plt.plot(C_QLBS.T.iloc[:,[200]])\n",
    "# plt.xlabel('Time Steps')\n",
    "# plt.title('QLBS RL Option Price')\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "\n",
    "part5 = str(C_QLBS.iloc[0,0])\n",
    "submissions[all_parts[4]]=part5\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:5],all_parts,submissions)\n",
    "C_QLBS.iloc[0,0]\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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M4LznJ/+wgbW7j6KqAV8x+nzeAu5+4Cn69+luiTkfUlJSCvUiJKYQJCSlsGTr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\ns6ewqM6fX+Xs1Erqo427z3T3ge7ez93vDZY9Ep8Zx90vcfe27j46eIy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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f068008d1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# add here calculation of different MC runs (6 repetitions of action randomization)\n",
    "\n",
    "# on-policy values\n",
    "y1_onp = 5.0211 # 4.9170\n",
    "y2_onp = 4.7798 # 7.6500\n",
    "\n",
    "# QLBS_price_on_policy = 4.9004 +/- 0.1206\n",
    "\n",
    "# these are the results for noise eta = 0.15\n",
    "# p1 = np.array([5.0174, 4.9249, 4.9191, 4.9039, 4.9705, 4.6216 ])\n",
    "# p2 = np.array([6.3254, 8.6733, 8.0686, 7.5355, 7.1751, 7.1959 ])\n",
    "\n",
    "p1 = np.array([5.0485, 5.0382, 5.0211, 5.0532, 5.0184])\n",
    "p2 = np.array([4.7778, 4.7853, 4.7781,4.7805, 4.7828])\n",
    "\n",
    "# results for eta = 0.25\n",
    "# p3 = np.array([4.9339, 4.9243, 4.9224, 5.1643, 5.0449, 4.9176 ])\n",
    "# p4 = np.array([7.7696,8.1922, 7.5440,7.2285, 5.6306, 12.6072])\n",
    "\n",
    "p3 = np.array([5.0147, 5.0445, 5.1047, 5.0644, 5.0524])\n",
    "p4 = np.array([4.7842,4.7873, 4.7847, 4.7792, 4.7796])\n",
    "\n",
    "# eta = 0.35 \n",
    "# p7 = np.array([4.9718, 4.9528, 5.0170, 4.7138, 4.9212, 4.6058])\n",
    "# p8 = np.array([8.2860, 7.4012, 7.2492, 8.9926, 6.2443, 6.7755])\n",
    "\n",
    "p7 = np.array([5.1342, 5.2288, 5.0905, 5.0784, 5.0013 ])\n",
    "p8 = np.array([4.7762, 4.7813,4.7789, 4.7811, 4.7801])\n",
    "\n",
    "# results for eta = 0.5\n",
    "# p5 = np.array([4.9446, 4.9894,6.7388, 4.7938,6.1590, 4.5935 ])\n",
    "# p6 = np.array([7.5632, 7.9250, 6.3491, 7.3830, 13.7668, 14.6367 ])\n",
    "\n",
    "p5 = np.array([3.1459, 4.9673, 4.9348, 5.2998, 5.0636 ])\n",
    "p6 = np.array([4.7816, 4.7814, 4.7834, 4.7735, 4.7768])\n",
    "\n",
    "# print(np.mean(p1), np.mean(p3), np.mean(p5))\n",
    "# print(np.mean(p2), np.mean(p4), np.mean(p6))\n",
    "# print(np.std(p1), np.std(p3), np.std(p5))\n",
    "# print(np.std(p2), np.std(p4), np.std(p6))\n",
    "\n",
    "x = np.array([0.15, 0.25, 0.35, 0.5])\n",
    "y1 = np.array([np.mean(p1), np.mean(p3), np.mean(p7), np.mean(p5)])\n",
    "y2 = np.array([np.mean(p2), np.mean(p4), np.mean(p8), np.mean(p6)])\n",
    "y_err_1 = np.array([np.std(p1), np.std(p3),np.std(p7),  np.std(p5)])\n",
    "y_err_2 = np.array([np.std(p2), np.std(p4), np.std(p8), np.std(p6)])\n",
    "\n",
    "# plot it \n",
    "f, axs = plt.subplots(nrows=2, ncols=2, sharex=True)\n",
    "\n",
    "f.subplots_adjust(hspace=.5)\n",
    "f.set_figheight(6.0)\n",
    "f.set_figwidth(8.0)\n",
    "\n",
    "ax = axs[0,0]\n",
    "ax.plot(x, y1)\n",
    "ax.axhline(y=y1_onp,linewidth=2, color='r')\n",
    "textstr = 'On-policy value = %2.2f'% (y1_onp)\n",
    "props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)                      \n",
    "# place a text box in upper left in axes coords\n",
    "ax.text(0.05, 0.15, textstr, fontsize=11,transform=ax.transAxes, verticalalignment='top', bbox=props)\n",
    "ax.set_title('Mean option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[0,1]\n",
    "ax.plot(x, y2)\n",
    "ax.axhline(y=y2_onp,linewidth=2, color='r')\n",
    "textstr = 'On-policy value = %2.2f'% (y2_onp)\n",
    "props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)                      \n",
    "# place a text box in upper left in axes coords\n",
    "ax.text(0.35, 0.95, textstr, fontsize=11,transform=ax.transAxes, verticalalignment='top', bbox=props)\n",
    "ax.set_title('Mean option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[1,0]\n",
    "ax.plot(x, y_err_1)\n",
    "ax.set_title('Std of option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[1,1]\n",
    "ax.plot(x, y_err_2)\n",
    "ax.set_title('Std of option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "f.suptitle('Mean and std of option price vs noise level')\n",
    "\n",
    "plt.savefig('Option_price_vs_noise_level.png', dpi=600)\n",
    "plt.show()"
   ]
  }
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