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Implementation of optimal execution using limit and market orders from Chap 8.5 of Algorithmic and High-Frequency Trading by Cartea, Jaimungal, & Penalva (2015) Cambridge University Press
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Liquidation with Limit and Market Orders Targeting Schedules(Chap 8.5)\n"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "This notebook implements the optimal liquidation of an asset using limit and market orders in a manner that aims to follow a given schedule as discussed in Chapter 8.5 of\n\nAlgorithmic and High-Frequency Trading \n(c) Cartea, Jaimungal, & Penalva, 2015 \nCambridge University Press\n\nhttps://www.amazon.co.uk/Algorithmic-High-Frequency-Trading-Mathematics-Finance/dp/1107091144/ref=cm_cr_arp_d_product_top?ie=UTF8\n\n## Introduction\n\nIn Chapter 8.5, Liquidation with Limit and Market Orders, we investigate the optimal strategies followed by a trader who wishes to liquidate shares using both limit and market orders, and simulataneously aims to track a given target inventory schedule. For example, she may be interested in liquidating shares but also in tracking the inventory scheduled followed by TWAP or a schedule such as that implied by the Almgren-Chris strategy.\n\nIn this case, the trader's performance criterion is\n\n\\begin{equation}\n\\mathbb E\\left[ X_T^{\\tau,\\delta} + Q_T^{\\tau,\\delta}(S_T-\\xi-\\alpha\\, Q_T^{\\tau,\\delta}) - \\phi \\int_0^T (Q_u^{\\tau,\\delta}-q_u)^2\\,du\n\\right]\n\\end{equation}\n\nwhere $\\tau$ represents the set of (stopping) times at which the trader submits market orders, $\\delta$ respresents the depth in the limit order book the trader posts their sell limit order, $X^{\\tau,\\delta}$ is the cash value of the strategy, $q_t$ is the target inventory schedule, and $Q^{\\tau,\\delta}$ is the trader's inventory.\n\nIn particular, the processes appearing above satisfy the SDEs\n\n\\begin{equation}\ndX_t^{\\tau,\\delta} = (S_t+\\delta_{t^-})\\,dN_t^\\delta + (S_t-\\xi)\\,dM_t^\\tau\n\\end{equation}\n\n\\begin{equation}\ndQ^{\\tau,\\delta} = -dN_t^\\delta - dM_t^\\tau\n\\end{equation}\n\nwhere $N^\\delta$ is the counting process for filled limit orders and $M^\\tau$ is the counting process for submitted market orders."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# import pakacges\nimport numpy as np\nimport import_ipynb\nimport LOMO_target_helper as lth",
"execution_count": 1,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "importing Jupyter notebook from LOMO_target_helper.ipynb\n"
}
]
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# initial various parameters\nT = 60\nNdt = 6000\ndt = T / Ndt\n\nt = np.arange(0, T + dt, dt)\ntau = T - t\n\n# price jump sizes\nsigma = 0.01\n\nkappa = 100\nxi = 0.01\nalpha = 0.001\n\nlamb = 50 / 60\nNq = 10\nphi = 0.001\n\n# AC Solution\nphiAC = 10 ** (-5)\naAC = 0.001",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# get the target strategy -- Almgren-Chris in this case\n\nqAC = lth.AC_solver(phiAC, aAC, tau, T, Nq)\nlth.plot_curve(t, qAC, xlab =\"time\", ylab=\"Inventory\", title=\"AC target\")",
"execution_count": 3,
"outputs": [
{
"data": {
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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Optimal Strategy\n\nIn the chapter, we demonstrate that the value function admits a decomposition the ansatz as $H(t, x, S, q)= x + qS + h(t, q)$, \nwhere $h$ satisfies the the quasi-variational inequality ($QVI$) in equation 8.25 in Chapter 8.4:\n\n\\begin{equation}\nmax \\Bigg \\{ \\partial_t h - \\phi (q - q_t)^2 + \\frac{e^{-1} \\lambda}{\\kappa} e^{-\\kappa [h(t,q) - h(t,q-1 )]} \\Bigg \\} = 0,\n\\end{equation}\n\nsubject to the terminal and boundary conditions\n\n\\begin{equation}\nh(T,q) = - \\ell(q) \\enspace and \\enspace \nh(t,0) = \\phi \\int_t^T q_u^2 du.\n\\end{equation}\n\nThe optimal strategy is given by\n\n\\begin{equation}\n\\delta^{*} = \\frac{1}{\\kappa} + [h(t,q) - h(t,q - 1)], \n\\end{equation}\n\nand the optimal timing $\\tau_q$ of MOs (when the trader has $q$ assets) \nis the first time that\n\n\\begin{equation}\nh(\\tau_q, q-1) - h(\\tau_q, q) = \\xi\n\\end{equation}\n\nThe $QVI$ can be linearised by making the transformation\n\\begin{equation}\nh(t,q) = \\tfrac{1}{\\kappa} log\\, \\omega(t,q)\n\\end{equation}\nand we find that $\\omega(t,q)$ satisfies \n\n\\begin{equation}\nmax \\Bigg \\{ (\\partial_t - \\kappa \\phi (q - q_t)^2) \\omega(t, q) + e^{-1}\\lambda \\omega(t, q-1) \\;\\textbf{;}\\; e^{-\\kappa \\xi} \\omega(t, q-1) - \\omega(t, q) \\Bigg \\} = 0,\n\\end{equation}\n\nsubject to the terminal and boundary conditions \n\n\\begin{equation}\n\\omega(T, q) = e^{-\\kappa \\ell(q)} \\enspace and \\enspace\n\\omega(t, 0) = e^{-\\kappa \\phi \\int_t^T q_u^2 du} .\n\\end{equation}\n\nThe solution to this QVI is implemented in the helper file."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# Inventory q Vector\nq = np.arange(0, Nq + 1, 1)\n\n# solve the QVI for omega\nomega, exe = lth.hjb_solver(t, dt, kappa, xi, phi, q, qAC, lamb)\n\n# obtain the optimal time at which to execute market orders\nt_opt = lth.find_opt_t(exe, t)\n\n# Solve for delta\ndelta = lth.find_delta(kappa, omega, Nq, Ndt)",
"execution_count": 4,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Below, for each inventory level, we plot the time $\\tau_q$ at which the trader should submit a market order together with the target schedule $q_t$. For example, the trader currently has 4 assets, they will post a limit order but if it is not filled by $t\\sim20sec$, then they execute a market order."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# plot the results\nlth.plot_topt(t_opt, q, qAC, t)",
"execution_count": 5,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Next, for each inventory level, we plot the optimal depth $\\delta_t$ as a function of time."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_multi_lines(t[0:(t.shape[0]-1)], delta[:, 0:(delta.shape[1]-1)], xlab=r\"Time ($sec$)\", ylab=r\"$\\delta^*(t,q)$\", title=r\"Optimal Limit Order Depth\")",
"execution_count": 6,
"outputs": [
{
"data": {
"image/png": 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9JRCwQDLGdA9pHUYiMlpE5ohIrYhsFpGbRMSzh8dkiMgtIjJPROpEJOYRXUTuExGNcRvVMa+m7Q6bLNTUwEcfprokxhjTOdI2jESkEPgvoMCpwE3ANcCNe3hoNnAJUAss3MO2y4BJzW5r213oJBk7DnJyYN48qxkZY7oHb6oL0IorgCzgDFXdAbwmInnADSJyc2TZblS1SkSKVFVF5AfAtFaeo0ZV30l+0RPj87lz1c2frzQ0KH6/pLpIxhjTodK2ZgQcD7zSLHQexQ2oKa09UFX3+irFkUe6veoWLUp1SYwxpuOlcxiNwj2N9iVVXY97+i1Z7TqjRWSHiDSIyHwRaTXkOtMBB0BhIcx7K5zqohhjTIdL5zAqBKpiLK+MrEvUB7htUCcDFwAe3FOBh8TaWEQuE5FFIrKotLQ0CU/fOo9HOOxwYdEiuwKsMabrS+cwArfzQnPSwvL4dqz6F1W9Q1XfVNVZuG1Lm4BrW9j+TlWdoKoTevbsmejTt8kRR7iXlXj3HQsjY0zXls5hVAkUxFieT+waU0JUtQ54ERif7H231777Qq9e8NZbFkbGmK4tncNoGc3ahkRkIJBDs7akJEubI7+IcMQRwkcfQXV12hTLGGOSLp3D6CVghoj0iFp2LlAHvJnsJxORLNwefGl1AYcjjxTCYVhgF90zxnRh6RxG/wQagKdEZLqIXAbcANwW3d1bRFaKyL+jHygix4vIWcC4yO9nRW6DI7/nR2ZouFxEjhaRc4G5QH/gD53y6tpo8BAYOBDm2ak6Y0wXlraDXlW1UkSOBv4GzMZtJ7odN5CieXF7wkW7Axgc9fsTkfvvAPfhhlwpcB3QC6gH3gamqGpajewREY48UnjoIaW0VOnZ0wbAGmO6nrQNIwBV/YzWZ1BAVYe0ZVmz9fXAGYmUrTMdEQmjt95SzjzTwsgY0/Wk82k6E9G3r7DvKJj7utIFJpcwxpjdWBh1otqA8uraIBX18QfKtGnChg2wcmUHFMwYY1LMwqgTragMM/Olet5YH4z7sYcfLvh8MHeu1YyMMV2PhVEnOqDEodAPb20Mxf3Y3FzhkEOEt960i+4ZY7oeC6NO5HGEwwd4mbcx1K62n2nThJ07YXFajYQyxpjEWRh1siMGeNhSo6ysij+MDhwPBQUw93WbydsY07VYGHWyIwe4Q6Le3BB/u5HHI0yZ4s7kvWOHnaozxnQdFkadbFCew5A8YV472o0AjpomBIM2I4MxpmuxMEqBIwd4eHtziEAo/kAZOlQYOtR61RljuhYLoxQ4YoCXXQFYsr19bT9HTRNWrID16y2QjDFdg4VRChw2wIMj8FY72o0ApkwRvF547TULI2NM12BhlAIFfmFsT4d5m9rXblRQIBxyiDs9kI05MsZ0BRZGKXLkAA8fbAuzo6F9YXLsDIedO+Htty2MjDF7PwujFDligIeQwoLN7asdjR3rXpL8tVctjIwxez8LoxSZ0MdDrg/mtmOeOgDHEY45Rvj4Y9iyxQLJGLN3szBKkQyPcOQAD3PWtW9qIICjpwuOY7UjY8zez8IohY4e7GVLjfJ5Rfu6eBcXCwdNgNdfV4JBCyRjzN7LwiiFpg1ypwaas6597UYAxx7rUFkJi9LqYunGGBMfC6MU6p3jMKbEYc669rUbARx0EBQVwauv2uSpxpi9l4VRih092MOibWGq2tnF2+MRph8jLFkM27baqTpjzN7JwijFpg3yElbadfXXJscdJ4jASy9ZGBlj9k4WRil2YC+Hwkx4fX37242Ki4VJk4TXXlMa2lnDMsaYVGpXGInrGBG5WUTeEZHNItIoItUiskJEnhCR74lI/2QXuKvxOMJRA728vj5IuJ1dvAFOPFHYtcsuLWGM2TvFFUYiki0ivwRWAy8DPwUOAQqA7UAQGAacCfwdWCMiT4rI5KSWuouZNshDRT18sK39nRBG7w+DB8Pzz2u7xy0ZY0yqtDmMROQ7wArgD0AdcCNwDFCgqtmqOkBViwEvMBr4LvAkcDwwT0QeE5FByX4BXcFRg7x4BF5d2/52IxHhxBOFNWtg2edJLJwxxnSCeGpG/wbeBSaq6mhVvUlV56jqjuiN1LVMVe9T1fOAPsCPgcOBmckqeFdSmClM6ufhpTXtDyOAKVOFnBx44QWrGRlj9i7xhNEEVT1DVd+P5wlUdYeq/hUYDjweV+m6keOGelhZpayobP+pusxM4ejpwsKFSkWFBZIxZu/R5jBS1SWJPJGq1qvqskT20ZXNGOoF4OUEa0cnHC+EQvDKyxZGxpi9h3XtThP9cx3G9nR4JcEw6ttPOPhgd8yRdfM2xuwt2h1GIrJURB4QkZ+IyFQRyU9mwbqj44d6WbI9zJZdiU3tc+ppDtXV8MZcCyNjzN4hkZrRQOAC4FZgDlAhIisjY4x+JSLHiUivpJSymzgucqru1bXtHwALcMABMHwEPPOsEg5bIBlj0l8iYdQHeAkQYA2wCMjEHWP0e+AFYIuIbBSR2SJyo4icZt27WzayUBiWLwn3qhMRTjtN2LzJZvM2xuwdEgmjm4EpwBRVHaGqE1V1APAN3PFFAnwOZAAnAr8BnsIdMGtiEBGOG+pl4eYQ1Qm29xx2mNCzJzzztM3mbYxJf4mE0VnAo6o6L3qhqi5V1XOAG3CDaAQwCDgVd6Ds7ASes8s7fqiXYBheS2AALLizeZ98ivDpp7B8uZ2qM8akt0TCqAAoa2mlqt4E7AKuVdWNqjpbVW9U1dMTeM4u78DeDv1zhedWJRZGAMcc4w6CfeYZCyNjTHpLJIy+AI7awzb/Bc5O4Dm6HUeEk4d7eXNDiMr6xEIkO1uYMUN4e6Gy1a51ZIxJY4mE0T3AwSLyk1a2KQL6JfAc3dKpI7wEwiTckQHgpJMFjweeetLCyBiTvhIJo78DrwG3isiLInJo9EoRmQKcB2xO4Dm6pW/0dBicJzy3MvEwKi52rwQ7Z45SWmqBZIxJT+0OI1UNASfhTqB6HLBARLaLyCIRWQO8DmQBf01KSbsREeGU4V4WbApRXpd4gJxxhqAKTz9tYWSMSU8JTQekqgFVvQyYCDwIhIDxwADcNqXvquqfEy5lN3TqSC8hhRdWJ1476tVLOOoo4bVXlcpKCyRjTPpJytx0qvq+ql6kqn1xa0NZkctM3JfIfkVktIjMEZHayNVkbxIRzx4ekyEit4jIPBGpE5EWj74icqqIfCIi9SLymYicm0h5k2m/IocRBck5VQdw5llCMAjPWs86Y0waSvpEqaraoKoJH0FFpBC3N57ijlG6CbgGd6xSa7KBS4BaYGEr+z8cd3DuXNwLAL4APCIixyZa9mQQEU4Z4eXtzSG21SQ+cLVfP+HwI4SXXlJ27LBAMsakl3SetfsK3FrWGar6mqr+EzeIrhaRvJYepKpVQJGqzgCebmX/vwHeUtUfqepcVf0Z7qXUf5u8l/B12wMh/rJ1J1sa2zb33KkjfCjwbJJqR2efLdTXw3PPWRgZY9JLOofR8cArza4k+yhuQE1p7YGq2urRVkT8uGOkml/s71FgUkfNQF4dCvPHzTt4ubquTduPLHQY18vhieXJCaNBg4TJk2H2bKW62gLJGJM+0jmMRgFfuxifqq7HPf02KsF9Dwd8zfePO5eeA+yT4P5jGpnpY7jfy8tV9W1+zFn7ePm0LMxn5YnN5N3kvPMdGhts3JExJr2kcxgVAlUxlldG1iW6b2Lsv7LZ+qQ7riCThTsbqA62rR3o1BE+fA488UXyakdTpggvvqiUl1sgGWPSQ4eFkYh8W0TOT/CUV6yjpbSwPBn7l5aeV0Qui4yhWlRaWtruJ5yRn0kQeH1H22pHxVnC0YM9PL0iSDBJ1yY67zwhHIbHH7MwMsakh46sGd0HPACsE5H/bceF9ipxJ2NtLp/YNaZ4902M/Tf9vtv+VfVOVZ2gqhN69uzZ7icen5NBidfhleq2n6o7ex8f22uVtzYk51Rd7z7CMccIr71mc9YZY9JDR4bR/bgDYVcDPwPWxvn4ZTRrGxKRgUAOu7f1xGsVEGi+/8jvYWB5gvtvkUeEY/MzmVNdT0MbazpHD/ZQ6CdpHRkAzj7HnbPukUcsjIwxqddhYaSqMyMDYccDxcA5ce7iJWCGiPSIWnYuUAe8mWDZGnDHFzWfUfxc4G1VrU5k/3tyXEEmu8LKwl0Nbdo+wyOcOtLHK2uC7EjwontNiouFE04U3nxDWbfOAskYk1rtDqNIe1D/tmyrqtWq+nycT/FPoAF4SkSmi8hluBfsuy26u7eIrBSRfzcr2/EichYwLvL7WZHb4KjNfgdMFZE/i8hUEbkZOAF3cG2HOrxHJtmO8EocverO3sdLfSh5Y44AzjxTyM6G++61q8EaY1IrkZrRg8DFySpIc6paCRwNeHCvDnsjcDtwfbNNvZFtot0BPBFVvicity+vv6Sq83GvVjsdeAU4BThfVV9N6guJIcsRpub5ebW6jnDrQ6K+NK6Xw+hih4c+DyStHHl5wrnnCkuWwJLFVjsyxqROh3btjtRGftfex6vqZ6o6TVWzVLWvqv4mMlt49DZDVHVmjGUS43Zfs+2eUdUDVNWvqqNU9dH2ljVex+VnsSUQ5sPatoWLiHDBaC8fl4b5uDQ5HRkATjhR6NMH7r03TChkgWSMSY24wkhEvikiI0RE9rw1APsD18ZfrK7v2PxMMgSeq2zbbAwAZ4z0kemFBz9LXu3I5xMumumwfj389zULI2NMasRbM3oY99IQVbhjcY4RkYtFZLyI+GJsn4Pb7mOayfc6TM3LZHZl20/V5fvd6xw9vSLIrsbkBcekSTB6NDz0kFJba4FkjOl88YbRT3EDaRPuANHDgDuB94GdIrJERO4Wke+LyIW4V3pdl8wCdyUnF2SxORBiSU1jmx9z4WgfNQF4JokdGUSE717sUF0Ns56wMDLGdD5vPBur6m1NP4tIGHdg69u4F9QbD4wh0oMtyg8SK2LXNaMgE/96eLayjgm5/jY9Znxvh/2KHB78LMC3RseqjLbPyJHC1KOEZ59Vjp6u9O/f1jOxxhiTuEQ6MNwMvKiqd6nq91R1ItADGAtcBFwNTFHVfyShnF1SD4/DUXmZPF/V9lN1HdWRAWDmTCEjA+78V5g9THxujDFJ1e4wUtVfquqsZstCqvqJqj6gqn9W1XmJF7FrO6Uwi62BMO/HcaruzH18ZHnhnk+S15EBoLBQuOBbwocfwsIWL0tojDHJl86zdncLx+Rnkhlnr7p8v3DOvl6eWRGkrDa5A1aPP14YOhT+fXeYujqrHRljOkebw0hEshJ9smTso6vJ9ThMy8/k+co6QnGcGvvumAwaw/DAZ8nryADg8QhXfM+hvBwee9TCyBjTOeKpGa0RkasiV0mNi4iMFZFncXvjmWZOL8xmezDMvJ1t7wU/stBh6kAP//k0QGOSB6uOGiVMny4895yydq0FkjGm48UTRq8CtwFbROQOETmqtZqOiAwTke+JyNvAEtyODXMTK27XdEx+Jvke4Yny2rged8kY99ISz69Kbu0I4KKZQk4O/O2vNjODMabjtTmMVPXbwERgEXAZ8F+gWkQ+EpGXReQREXlaRN4SkW3ACuDvwBDg18C+kfngTDN+RzilMIsXq+rZFWp7G9DUQR6G5Qt3fxJIeu+3vDzh0suEFSvguecsjIwxHSuuDgyqukhVj8W97s8twEfAaOBY3MsvnAocHtn8KeB8YJCq/jFy2QbTgrOLsqlX5YWqtndkcES4+Bs+PtweZvG25M+8fcQRwiGHwMMPKVs2WyAZYzpOu3rTqeqKSNfug3GvvLovMBk4EOivqr1V9WxVfVRVk9v/uIuakJPBEL+HWRVtDyOAc/b1UeCHOz5se9fwthJxOzP4fPC3v4UJJ+my58YY01zCXbtVtTYSTu+o6kequiUZBetuRISzi7JZsLOBjY1tbwPK8QkzD/Dx0poQKyqTXzsqLha+8x1h6VJ45WULI2NMx7BxRmnkzKJsFHgqztrRxWMyyPTCPzqgdgQw/Rhh3Di4915ls52uM8Z0AAujNDLY72VibgaPl9fG1SGhOEs4fz8fTy4PsmlX8mtHIsKPrnJP1912W5hg0ALJGJNcFkZp5rzibFY1BHl7V3y1nCvGulSXlFsAACAASURBVJOm3vlRxzTRFRcLV37fYcVyeOwxCyNjTHK1KYxE5DARGRD5uZ+IHNaxxeq+Ti7MIs8jPFhWE9fjBvRwOH2Elwc/C1BR3zFhcdhhwrRpwqwnlM8/t0AyxiRPW2tGGbgDXoncJ+/aBeZrsh2Hs4qyeaGqjopgfLNyX3mgj7og3P1xx7QdAVx6mVBSArffFrYL8RljkqZNYaSqc4HtIvI/QLmqvtGhpeqiajXEq4EydmrrveW+VZJDo8IT5fF1ZNi3yMNJwzzc/XHH1Y6ys4Wrr3YoLYW//VXtUhPGmKTYYxiJyFwReR04FPgVcEjUMhOHLeEG/tawgfnBqla32y/Lx4ScDB4oq4n7YH/NwRnUBDpm3FGT/UYL37pQWLBAeeEFCyNjTOL2GEaqepSqTgPeAf4IvBe1zMRhmJPFICeTuYGKPW77rRK3I8M7cXZk2LfIw6kjvNzzSYDSJF9eItrppwsHHwz33qN88YUFkjEmMW3twDAV6KWq1wLFkd9NnESEo7xFLAvXsCXc+uxITR0ZHoizIwPA1RMyaAjB3z/ouMkvHEe46scORUVwy81hduywQDLGtF9bOzAEgWsiP18DJPd6193IFG8hArwRbL12lO04nFuczezKOrY2xvfnHlHocNY+Xu7/NMDWmo6rHfXoIfz8Fw6VlW6HBpvd2xjTXm3twDBfVTdEft5klxNvvxIngzGeXOYGKvbYHnRxz1xCwH/aUTv6yYQMggp/XtRxbUcAI0cKl10mLFkC999vYWSMaR8b9JoCR3mL2KqNLAu3HjKD/V6Ozc/k/rIa6uOcpHRwnsOFo3089HmwQ+asizbjOIcTThCeeVp5fU7HPpcxpmuyMEqBSd4CMhDmBir3uO2lvXKpCIZ5uiK+C++B23aU7YPfv93xV++4+BLhG2Ph73+3AbHGmPhZGKVAtng41FvA/GAljdp6TWJybgajs7zctX1X3N28i7OEH47P4LV1IRZsSv7VYKN5vcLPf+7Qsyf87x/ClJZaIBlj2i6uMBIRv4hIRxWmO5nuLWIXId7ew5gjEeHinrl8Xh9kQZzdvAEuHuOjf65w48JGwh08QLVHD+HX1zkEg3DDDWF27rRAMsa0Tbw1o78C60Xky+mAROQSEflARDaLyCIRuV1Exia3mF3PNzw96CMZvBos3+O2pxdlU+x1uGPbzrifJ8sr/GpiBkvLwjy5vGNrRwADBwq/utZh6xb4n9+HaWiwQDLG7Fm8YTQdmN909VYRmQncCYwF+gDjgauAJSLyLxHxJrGsXYojwrG+Yj4J7WJTuL7VbbMc4dJeuby+o4FPauOvHZ020su4Xg7/804jOzohHMaMcacMWrYM/nSrdfk2xuxZvGHUD1gb9ftvgEeAgUAmsB9wLbAJuAR4KPEidl1He4vxAK8G9lw7mlmSQw9H+OvWXXE/jyPC/x7hp7RWufX9ju3q3eSww4VLLhXefRf+9U+bw84Y07p4wygENNWKhgENwIWRsUeNqvqFqv4ROACYDZwlIqcntcRdSKHjY6KngDmBCgJ76MiQ73W4qGcOz1fVsao+/pkVxvbycOFoL/csDfBpWeeMWT7pJIczzxReeUW59x4LJGNMy+INo1KgZ+TnycBs1d2Poqq6AzgXWA9cnlAJu7gZvmJ2EOSdYPUet72sVy5+gb9vi792BPCLiX4K/HDtvIYO78zQ5MJvCyeeJDz7rPLA/RZIxpjY4g2j94ETRKQImAlsbmlDVW0AngEmtLt03cBYTw96SQYvBcr2uG1Pn4fzS3KYVVHLpsb4OyMUZgq/PtTP+1vDPPFFx3dmALc34KWXCjOOE558Unn0EQsjY8zu4g2jO4EBuDWko4ArRKSkle1DQG47y9YtOCKc6CthaXgXq0N7Hth6RS/3z/l/7Wg7Ajh3lJeD+zjctLCB7R04q3c0EeGKK4SjjxYefVR57NGw1ZCMMV8TVxip6mvAd4DPgbm4p+LeFJETmm8rIgXAWbRSezKuY3zF+HGYHSjd47YD/V7OL87h4bIa1jXEX7txRLh1aia1Qbj2rYZOCwXHEb7/A+Goo4SHH1b+c5+dsjPGfCXuGRhU9X5VPUBVp6vqx8D1wDORcUb3isiNIvIX4FPcXnZPJrnMXU6ueDnaV8SbwUqqwnvunPDjPj3wCvxpy452Pd/IQodrDs7gxTUhZq/qnNN1AB6P8KOrhONPEJ5+WrnjH2rdvo0xQBKmA1LVWcBUYDtwEW537x8CfYE3gRsTfY7u4CRfT4IoLwf33HbUJ8PDzJ65PFlRx/K69l2z6IqxPsb1crh2XgPldZ0XCI4jXH65cNZZbi+7229TgkELJGO6u6TMTaeqC1V1HO7g1wtxe9AdoarTVLV9jRvdzAAnk4M8ebwUKNtjN2+A7/fOJcsRbmln7cjrCLdN9bOz0e1d15mnzESEC7/t8O2LhHnzlJtuDFNTY4FkTHeW1IlSVfUTVX1IVe9S1QXJ3Hd3cIqvJ5Ua5K3gnmfzLvF5uLRXLs9X1fNhTfsGso4q9vDTgzOYvSrI453Uuy7amWc6/PBHwtKl8Iufh9m+3QLJmO4qrWftFpHRIjJHRGojbVI3iYinDY/Lj7RfVYpItYg8JCLFzba5T0Q0xm1Ux72i1o3z9GCIk8mTjdvaNA7oe71zKfY63LCput01myvH+Zjcz8Ov5zWwqqrzr0U0fbrDDTc4VFTAz34aZsUKCyRjuqO0DSMRKQT+CyhwKnAT7iXP29IG9RhuO9YluOOhDsYd89TcMmBSs9vahAreikpqeYoPqCJ2F24R4WxfHzZqA++E9jwINs/j8PO+eby7q5EXqlqf364lHkf4v6P9+D3w/f/W05iCDgXfGCv8v5sdMjLg2l+FefNNu0CfMd1N2oYRcAWQBZyhqq+p6j9xg+hqEclr6UEiMgmYAVykqk+q6tPAt4DDRWR6s81rVPWdZrf2HdXbwEH4lC28z7oWt5nsLaCf+Hm8cWubajvnl2QzKtPL7zZVx3012Cb9ch1uPSqTj0vD/PHdzpm7rrmBA4VbbnUYMQJu+5Ny111h69hgTDeSzmF0PPBKZGqhJo/iBtSUPTxum6q+1bRAVd8D1kTWpUw+WexHHz5gPY3EbqPxiHBmRm9Wh+tYEtrzJSO8ItwwIJ/1jSH+vb39fUWOH+rlov29/POjAC+t6fz2I4CCAuF3v3c4+RTh+dnKb64LU1FhgWRMd5DOYTQK9zTal1R1PVAbWdfmx0V8HuNxo0Vkh4g0iMh8EWkt5JJiIkOoJ8jHbGpxm6neQkrExxONW9u0zyl5mRyTl8mft+5ka2P7J0G9frKfcb0crppTz4rK1Jwq83qFSy5xuOYaYdUquPonYT780ALJmK4uncOoEIh1GdTKyLpEH/cBbhvUycAFgAd4TUQOibVTEbkscvHARaWle54poSUDKKQf+bzLGpTYB1mfOJzh681n4Ro+DLat6/aNA/IJqHL9xj23NbUk0yvcNSMTv0e4+OU6djWmLgSOnOJw8y0OOTlw/W/D3HtPmEDAQsmYriqdwwiIebSWFpbH9ThV/Yuq3qGqb0YG7k7DvQ7TtTF3qHqnqk5Q1Qk9e/aMtUmbCMJEhlJODatoOdSO9RVTIj4eaNzSprajoZlerurTg+eq6phT3f5mr/65Dv881s+aauXHr9d32uzesQwZItx2u8NxxwnPPKP8/GdhNm60QDKmK0rnMKoECmIszyd2zWdPjyto7XGqWge8iHu12g41mr7k4ucd1rS4TYY4nJfRlxXh2jb1rAO4sncPRvi9/GpDFbXh9p9mO6y/l+smudMF3fxeajo0NPH7he9d6XDttQ6lpfCTH4d55mm7eqwxXU06h9EymrXxiMhAIIfYbUItPi6ipbak5jr8KOfB4WCGsJoyttBy0EzzFtFf/DzYuIVQG2oofke4eVABGxpD3L5lz50fWnPZN3xcsJ+X/1sS4JHP2zflUDJNPFT4v786jB0H996r/OLnYdautUAypqtI5zB6CZghIj2ilp0L1OHOedfa4/qIyOFNC0RkAjAssi4mEcnC7W23OJFCt9XBDMaPl/msbHEbjwgX+PuyIVzPm8GKNu13Ug8/5xVnc8e2Xe2emQHcMU9/OMLPlIEefvFWA29uSE0Pu2hFRcKvf+1wzU+F7dvdzg0PPRSmMYVtW8aY5EjnMPon7mXNnxKR6SJyGXADcFt0d28RWSki/276XVXfBl4B7heRM0TkNOAhYL6q/jfymHwRmScil4vI0SJyLu4lMfoDf+iMF5eJj4MZzOdspZSWazGTPQUMd7J4sHELDW2Ysw7g+v759PZ5+OHaSuraOfYIwOcR7jw2k5EFDpe9Ws/STrpceWtEhCOPdPjb3x2OOEJ4/DHlB98P8+47dkkKY/ZmaRtGqloJHI3by2027oDX23EvWRHNG9km2jdxa0/3APfj1nZOj1rfgHuBwOtw24nuxG1PmqKqi5L6QloxkaH48LCAVS1u44hwsb8/ZRrg6cC2Nu033+tw2+ACVjYE+ePm9veuA+iRIdx/YiY9MoTzZqeuy3dzeXnCT652uOl37swNf/hDmBtuCLNhgwWSMXsjsW+T8ZswYYIuWpSczHqFz3iPtfyAqRSS3eJ2/69+De8Hq7kjezQ9nYw27fvaDVXcW1rDkyNLmNzDn1A5V1WFOeOZOjwOPH1aFoPz0ud7TDCovPSS8sjDSn09HHeccM45QkGhpLpoxpgoIrJYVSfEWpc+R5RuajLDcBDmsaLV7WZm9APgP41tv3Dudf3yGOp3T9dVBhOr0QwvcHj05Ezqg8q5z9WxeVd61JDAHSh78skOd/zTYfoxwksvKZddFubBB8Ps2mVftozZG1gYpVgPMpnAYD5iI2W0PJ1Pb8fP6b7evBWs5LNQ26b9yfY4/GNIEWXBEFetrUx4zNB+xR4ePimLinrlzGfr2LAjfQIJID9fuPJKh7//w+GQQ4QnHlcuvyzMrFlhamstlIxJZxZGaeBwhuPDy1y+aHW7MzN60VN8/KNhQ5suwAcwLieD6/vn89qOev6ZwNx1X+6vl4fHTs6iql457Zk6VqZJG1K0fv2En/7M4fY/O+w7Ch64X7nkYremVF1toWRMOrIwSgM5+JnEUD5nK5taGc+bKR6u8A9kfbieJwPb27z/7/TM4eSCLP6waQfv7WpIuLwH9vYw69QsGkNwxrN1fFae+l52sQwbJvz2tx5u/ZPDN8bCrCfcULrzzjDbtlooGZNOLIzSxKEMI5sM5uxhXO7B3nyO8BbweONWNoTbNu2PiHDr4AIG+T1ctqaCLQlMptpk/xIPT52WhdeBM5+pY8Gm1I9DasnIkcIvf+n5sjv4yy8pl18e5ve/D/HhB0o4ge7vxpjksDDqRKphNgaWE9LdD9x+vBzBCNZSznJa78J9ScYAMnH4e/36NrcD5Xkc7hlWzK6QMnN1eULTBTUZWejw3OlZ9M5xOO/5eh5flvqZGlozYIDwo6sc7rzL4eyzheVfwPXXh/nB98PMnm2dHYxJJQujTlQZ3saHDXNYF/g05voJDKaEXF7hM4K0XHspdHxc7O/PZ+EaZgfaPoP4qCwfdwwt5JPaAD9eW5WUSVAH9HB49vQsJvXz8OO5Ddz8XkPaDz4tKREu+JbDv+9x+MnVQm4u3H2XMvOiMLfcEmbJYrW574zpZBZGnajI05eenoGsaFxCQHdvu/HgMIPRVFLb6iSq4M5bd4gnn/80bmZtqK7NZTgmP4vr+ucxu6qOWxOcv65Jvl948IRMvjnKy58XB/juy/XsaEj/g7nPJ0yd6nDzLR5uu93h2BnCRx8qN94Y5uKLw/znvjBr19jMDsZ0Bhv02g6JDHqtCpUyv24WI30Hsa8/5qWTeJxFrKKM7zOFPLJa3Fe1Bvhh7TLyxcufsvYlQ9r23UJVuWZ9FY+U1/K/A/OZ2TO3Xa8l1n7//UmAm95uZGAP4e4ZmexX3HxyjPQWCCiL3oc5r4dZvAjCYejXHyZPFg47TBg61G2DM8bEr7VBrxZG7ZDoDAyL619le3Ad07IvwO/sPutCJbXcwZvsQ2/O2sMVLRYFq7mpfjWn+HpyiX9Am8sQVOWS1RW8Wl3PP4YUclpRy7M/xOvdLSGueLWe6kbl/x3p56x9vHvlAbyqSnn7bWXhQmXpJ24w9e0LkyYLEyYIo0aBx7P3vS5jUsXCKMkSDaNd4SrerH2Uwb79OcB/RMxt5rGCuSznHA5iFH1a3d+/GjbwQqCMX2UOZZI31qWcYqsLK+evLGNxTSP3DStmWn5mXK+jNdtrw1zxaj3vbAlz8nAvfzzST2Hm3nvgrq5W3nlbWbBAWboUQiHIyYEDxwsHHQQHHSTk5++9r8+YzmBhlGTJmJvuk/o3WR/8nCOzzqGHp2i39SHC3M0Camjge0whC1+L+wpomF/WrWBjuJ7bsvelv9P2UNkRCnPm8jJW1Ae4J8mBFAor//gwwC3vN9IzS7h9mp8jB3iTtv9UqalRPvoIFr2vLFmiVFaCCAwbBmPGCGPGCKP3h+xsCydjolkYJVkywqhR65hb8wh5nmIOzTwl5mmsLVRzNwsYS39OYWyr+ysNN/KT2i8ocLzcmrUPmdL2tpryYIhvrihneX2Afw8rZnoSAwng49IQP/hvPSurlG+N9vLrQ/3k+7vGgTocVtascYPp44+VZcsgGATHgeHD3XDa/wBh332hR4+u8ZqNaS8LoyRL1qzdawNLWdowj/GZx9LPOzzmNnNYxgJWcR4HM5Jere7vo+BOrq9fySRvAT/zD8GJo52mMhjmmyvL+LwuwL+GFnF8QcsdJ9qjNqDc8n4jd30coDhTuOnwDE4Zvne2JbWmoUH5Yhl88omydKmyfLkbTuB2hNh3HzeY9t1XGDzE2pxM92JhlGTJCiPVMPPqZtGoDUzN/iZe2f1UXJDQl6frLudIcmn9UhBPN27j3sbNnOnrzUX+fnGVpzoY5ryVZXxUG+CPgwq4sCQnrse3xcelIX7+ZgMfl4aZNsjDDZP9jCjsuiMM6uvdQFq+XPlimfLFF1AducSU3++e2hs61O2lN3SYMGgQ+LtIrdGY5iyMkiyZ1zOqCG1hYd0zDPONZbR/csxttrOTu5nPYIo5n4MRWj5YqSp3NGzk5WAZV/oHcpyvJK7y1ITCXLamgtd3NPDjPj34ed8eSa+9hMLKvUsD3PxeI/UhuHC0j6snZFCc1fUPwqrK9m3wxXI3mFavck/z1UWGijkO9O/vBtPQITBwkDCgP/TqbbUos/ezMEqyZIYRuJ0Z1gU/47Cs0yn0xO45t4h1vMhSjmE/JjGs1f2FVPl9/Wo+CO3gusxhTPDmx1WegCq/XF/Fw+W1nF2Uxc2DCsl0kn8gLKsN86dFjTzwWZBcH/xofAYzD/CR7eteB91wWNm2DdasgTWrlTVrlNVroLzsq218PujXz53SaMBAGDDA/blPH+soYfYeFkZJluwwCmojb9Y+hgcvR2SfjUd273GmKI+zmBVs50IOZTC798CLVqshro30sLs+czhjvD3iKpOqcvvWndyyZSfjsn3cPayI/hkd0xPui4oQv3u7kdfXhyjJEr5/oI8LR3e/UGpu1y5lwwbYtFHZsBE2blA2boTt290xT03y86FPH+jdR+jTG3r3gb59hN59oKgInA74ImFMe1gYJVkiYdRYswFf9oDdTn1tD67nvfoXGO47kP38h8Z8bD0B7mYBDQS4lMNbnZ0B3Bkarq1bSWm4kZuyRjDKE38b0ItVdVy1thK/I9w5tCjhy5e35t0tIW5b1Mi8jW4oXTnOxwWjffTIsINptMZGZfMm2LhJ2boVtm2FrduUrVugrOzrQeXzQXExlPSEkmKhpARKSqC45Kufe/SwWSVM57AwSrL2hlHjrtWUL/8H+YPOIrtk98D5qH4uG4LLODTzFEq8/WPuo5Sd/JuFlJDDTCbhpfUu3BXhAL+qW0G1Bvhd1ghGtiOQVtQH+M6qCtY2BPlp3zx+2CcXTwcevKJDKdcH5+/n4+IxPgbmdd2ODskSDCqlpbsHVFmZUl4O5eXugN1oGRluKBUVQ2GBUFAIhYVQWAAFhfLlzz3yrN3KJMbCKMnaG0aqSsXKfxGo2UDP0T/Dk/H12RKCGmBe7RMECTIl+2wyJHbN5wu28hiLOYB+nM64Vjs0gDsG6dq6FezQINdlDov7lB3AzlCYn62v4tnKOibmZvDXwYUM9HfsANaPtoe48+MAs1cFCSscP9TDzAN8TOrniavbuvlKKKRUVbmhVFYGZaVuSJWWQUW5u66yCupjzL3rOO4pwYICN6wKCoS8fMjLg7wekJcn5OW5oZWXB7m5dorQfJ2FUZIlcpou2FBO2ee3kpE7nMLhF+92eqQ6VMqCuqco8Qzk4MzjWzx9Mp+VvM4XTGIYx7DfHp+3PNzIb+tXsTXcwC8yh3JInJ0awA3TWRV1XLuhCgF+P7CAs4uyOvwUz+ZdYe5dGuChzwJUNcCQPOGbo3ycM8pLnxyrLXWEujo3mKoqiQSUO9NEVaX7c1UlVFbCjh3Q2Bh7H47jBlJeJJzckJJIcDUtc3/vkeeeLszJsQDryiyMkizRDgw12+ezY+Mz5A8+l+zig3dbv6bxYz5tXMCojEMZkXFgzH0oykt8yiLWcSyjOZShe3zeHRrkxrpVrArX8n3/II7xFber/OsbgvxgbSXv1zRyZA8/Nw8qYHAH15IA6oLKi6uDPPJ5kIWbQzgC0wZ5OG2ElxlDveR08w4PqdLQoOzYQdTtq993xli2Y8fupwqbNAVYjx7uLS/PnbmiKayafm8KsLwekNsDvF577/cGFkZJlmgYqYapWHEHgdrNlOx3NV5/cbP1ypL6V9kSWs0hmSfQyzs45n7CKLNYwjK2chpj+QZ7nrW7VkP8sX4NH4Z2crqvF9/O6Neu9p+wKv8pq+EPm3YQVPhp3x5c2iuXjE76VrumOsyjnweYtTzIlhol0wvTB3k4dYSPaYM9ZNnBKW2pKrW1kbDa2XSv7Pza75FlUb+3VAMDyM5uCqqmm3z1e15UqEWFnA0u7nwWRkmWjK7dwYYKypbdjtdfQvE+30ecr9csghpgYd3T1IZ3cnj2GeQ6hbH3Q4iHeZ91lHNqGwMppMpdjRt5MVDGwZ48rskcQnYcc9lF29wY4toNVbxSXc8wv4ff9s/n2PzMTuudFVbl/S1hnl0V5PlVQcrqlGwvHDnQw/TBXo4e5KG3ncrrEppqYDt3wI4YYbUzUgNzg8y91da2vL+MjK9qVz1i1LjcIJOvhVx2tvU8TISFUZIla5xRXeUnVK35Dzm9ppA34OTd1teGdzK/bhY+/ByWfXqLHRoChHgkzkACeKGxlLsaN9JX/Pw8cyhDPe2fj+6/1fXcuLGalQ1BDsvN4PoB+YzJzmj3/tojGFbe3hzixdVBXlsXYvMu97M9rpfD0YO8TB3oYWwvB6+1SXQbgYCya1d0WLkhtmNny7Wympqvd4+P5vFE177czhzFxUJRsTumq7hYKI78nLkXXzKlo1gYJVkyB71Wr3+K2rKFFA6bSWbBAbutrwht4Z262eQ5xRyadUrM+evg64F0ImMYz6A2Pf/S0E5urV/LTg1xqX8AM7zF7f7mF1DlwbIabtm8k8pQmBMLMrm6Tx6js1u+/EVHUVU+rwjz37UhXlsXZMm2MArk+ODQvh4O6+/e9i9xrGee+ZpwWKmpaXbKMNLm1VTj2hEJsMpKKK+I3fswJ8cNpaIid1xXr57Quzf07i306u2O/+punTUsjJIsmWGk4QDly/9BsH4bxfv+EF9W39222Rpcw6L6V+jpGcDBmcfjtHBKLUCIJ1jMSko5kpFMYeQeu30DVIUD3N6wjg9COznMW8D3/APJizELRFtVB8PcuX0Xd23fxc6wckIklPZPQSg1Ka9za00LNgWZvynEqir3c1/gh4N6exjf28NBfRwO7OWxQbYmbrW1SkUFVJRDeYXbXd79/avxXRUVEH249XqhVy933sHevd2pnQYOFAYMcJd3xTFdFkZJllAYla+DokHu1dgiQo3VlH3xF0Q8lIz6MY5394Gp6wOf83HDG/T1DudA/3Qcid0OEiLMC3zCh2zkQAZyAgfgYc9tJmFVngps4+HGreSIh+/5BzI5jqvGxlIVDHNXVCgd2cPPZb1yOSrPn/LayNaaMAs3hViwKcSSbWGWV7o1JwH2LXIY39thXC8Po4sdRhU53X5qIpO4QCAyIHkbbNvmzke4betXP+/c+dW2GRnuhLlNcxEOGiQMH+YG197cZmVhlGTtDqPNn8Jzv4HDL4EDTvjaqsaa9ZQv/we+7IEUj7wMcXavRaxq/JDPG9+mj2cY4zOnt1hDUpQ3WM48VjKYIs5iPDl7uPREk7WhOv7SsI5V4ToO9xZwScYAimKUJR5VwTD3l9Vwb+kutgbCDPd7ubRXDmcWZZPrSY/OBTsalA+2u8G0eFuIJdtCVDW46xyBYfnC/iXuab0Dih32LXLokyN79YHBpJemuQib5iDcsFHZuMGdi7DpMJ2bC8OGw/BhwvARMHKk0HsvCigLoyRrdxhpGF76X1i/GE66AQZ842ur6yo+pGrtQ/jz96Nw2EVIjLBZ3fgRnzUupLdnCOMzj8XTSi+4T9jEbD4mmwzO4SD60baaTjBSS3q0cSs+hG9m9OFkXy+8CX7gA6rMrqzjzu27+Kg2QJYjnFKQxXkl2RySk5FW/1CqysadytLyMJ+Whfi0LMxn5WE27Pzq/yXHByMKHEYWOowocBgRuR+SL2R0wVMsJjUaGpT162HVKmX1Kvd+7dqvLtpYVAT77+9e6n7//YWBA9O3LcrCKMkSOk3XWAtP/QJqq+CsWyDv65eMqCldwI4NT5NVNIH8wecgMU7HrW1cytLGeRR7+jMhcwY+abnWs4VqHmcxu2jgWPZjAoPb1I4EsDncwN0NG1kUAjCrUwAAHzdJREFU2sEA8XOxfwDjPYlf30hVWVIb4OGyGp6trKMmrAz3ezmnOJtTCrMY0gkDaNurqkH5vDzM8oowK6rCrKwMs7Iq/GXPPeD/t3feYXJUV6L/neru6enJGo0ySigghBAIC4yIIphgTLANBvwZlsWGt/Yu9ltjbGCxTbD1jP0M2HgxZne9mN1lgSVnkUSyiCJLKCCEEkojjSb1zHQ6+8etnqkudU/SzHS3dH/fV1NV955765yumjp1MwGBsRXChEqHCVXChCp3X+kwsUoYHrElKsvuEY+bUtSK5cqyZbB0qWmbAjNl05xDhLlzYc4coaKicJ4164wGmN3uwNC4CR64Aspq4KwFUFqVEd286VlaNi2krG4eVeO/mtUhbYiv4P2OF6lwqjms9DQiTu755qLEeJj3+IRtTGUEZ3BQjyvGenkr0ci/dGxgs8aY5VTwrfAYZgYqem9vN0STKR7b2cbd9VHebDWjGmeXhTijJsLpwyJMKGDH5KU1rqz2OKe1Tcq6phTrmpRtbZn/Y5EgjK801XxjKoQx5cLocsfdm/PaiOS9Xc1SPKQXbfxoqfL+e/DOO2a8lePAzJlw5FHCkUcK1dX5faasMxpgBqQ33ecfwePXwfDJcMZ1EOoa46OqNH/+JK1bFhEZfijVE87J6pDqExt4u30hAQlyaOmp1ARG5rycorzFWp7lY8IE+QoHMoPsC/llI64pnolv5974ZnZqgrmBKs4vGcO0QFnf7O6G9R0JntjZxqMNbbwbjQMwKxLixOpSTqwu5eCy0KDOFj5YROOmym9tU4p1zSnWNynrm1NsblU2typbokrK929Y4sCocmFkmVAX6dqGRzLP6yLCsFIhUKDVMpb8kEya5e6XLFHeeN1U8wUCcPAcmD9fmDdPCOWhU451RgPMgHXtXvM6LPw1jDsQvnwNBLo6CqgqLZufpWXTM5QOm0PNpPOytiE1J3fwZvuTdGgrB4SPYkJwZrdVQFtp5mHeYzNN7McoTuWAHtdF8tKuSZ6I1/NAbAstJDkwUMHXQqMGpPrOy7qOBI81tLGwsZ0lrTFSQG3Q4fiqMMdXlXJkZZiRof7NGlFoJFLKtqiyyXVOn7cYR7Wp1YRvb1Pq25Tt7bs6LTA9AGtLhdoIVIeFGnerDgvVYTrPa0rFE29kbdvW3sFna5SXXlZefkmprzeDdU8+RTjlFKG2duieAeuMBpgBXel1+fOw6FaY8AU4+ccQzKw+a9myiOaNT1BSOZVhky/ECe5aEolpO++2P8e25HrGBadzYPiYnINjwXT/fp01vMRKHIT57MehTOxVF/A0UU2yMF7Po/FtbNc4E51SzgyN5OjgMMI5up33lx2JJC81dfBcYzuLmtppSJpndlppkCMqwhxRWcIRFWHq9hDnlIuUKg3tsKPdOCezpaiPmuOdHdDQrjR2KDs7zL6pm/ncAMIBqAgJlSVQXiJUhqCiRLrCQkJlSeZxhStTHoKykBAJQlnQ7G0JrbBJpZT33oXHn0ix5G0z1ulLJwnnnCMMHz749846owGm384oEYd7/whfvRjKPG0uyxbCS7fDuFlw6tUZVXYA0e1LaFx3H4GSWmqnfptguG6XrFWVVfElrIy9RblUc3Dp8QwLdF8N10CUJ/mI1WxjOOWcyAymM6rXHRzAVN+9nGjgofhW1qXaKSfA8aFaTg4NZ4LT/+mFcpFU5YNonMXNHSxu6eCNlhitbnFhSjjIIeUhDikvYU55CTMjIUJFWK03kCRSxiHt9DipnZ3OCppjSktMaYmb49a40hyjM6wlprTnmGE7G+EAlAWhNCiUhSASFMqCHqflcV7p+EjQlfOcp+W88ZGgyd92/hgYNn2uPPSw8tyziuPAaacJ554nlJUN3u9rndEA029n9PE7cPWFMGUmXPsvUOFZU2jFIlNCGjnNOKRI5npDHc2rafj0LwDUTDqf0ursaxjVJzbyfscLtGkrU0MHM63k0G67fyvKKrbyHB9TTysTqOUEZjCe7BOz5sxHlaWpVp6O17M4sZMEyv5OOfNDtRwZrNmtGR26I6HKh9E4f23u4K3WGO+0xqhPmInFSgUOLCthTnmIAyIlzIwEmVYaImy/3vtEPNnlmFo8ziqaMO1h0YRZ3iMad/dueJsb3haHqC8+Ld/Xt49AVueV4bg8jqwsR3j2PMy+NMhe1Xlky2blnnuVRS8ow4bBd77jcMSRg+P0rTMaYHarmu7NF+BXP4DxU+H6f4Pq2q641Yvh+VugbJhpQ6odn5E00V5Pw5q7SLR9Tvmo46gce0rWdqS4xljW8VfWJ5ZTITXMCh9NXbD7yVNTpHiH9bzISqLEmMxwjmYak+j7mkeNGuf5+A6ej+9gvbYTAA4JVHFMcBiHBauJ9HOG8N6gqmyIJXk3GuOd1jjvtMb4MBqn3X3Og8DU0iD7R0LMjITYPxJiammQfUoCRdk5ophRNaWuNr/z8u57ER7NCM+UjSbI2s7WE6UBXMeU3WH5HVyZJ7w8BFVhobrEtNlVue13ZcHCLtWtWKHc/scUn34KxxwjfPd7A19Kss5ogNntNqN3XoEF/wAjxsBPb4exk7ritqyEpxZAMgYn/CNMylx8T1NxmjY8QrT+dULlE6mZeC7B0uy96LYk1rK04xWi2szY4FT2L5lHxOm+S3aMBEtYx2I+pZUOJlDLPCYzjVE4fai+A/OyWZNq46VEA68kGqjXOCGEgwKVHBas5tBANcN3c3aH3pBU5dOOBB+3xVkajfNxW4Jl7XE2xrrqn8ICk8JBppQG2TccZGppkCnhIJNLg9QGnIJ+iVhyo6rEUnTv2Dyltszw3jvFWI5Zvr0EBKrcDiVVJeI6LNP5ZHhEqCsTRkSczl6TI8pM/FA+e8mk8sADyn/frYwcCVdd7TBp0sBd3zqjAWZAOjAsWwK//Hszz8eVv4PZh3fFNW+DpxdA/RqYfQYcfkFGTzuAth3v0rj+QTQVp3LMSZSPOjZrKSmpCVbH3+WT2LuAMDl0IFNKDqZESrtVL06Sd1nPYlbTRDs1RJjLROYwngh9XxoipcqyVCuvJ3byRqKRLWpa1qc5ZcwNVnFQoJLpTvluz/LQF3YmUixvj7O6PcHq9gSfdiT4pD3B2o4ECY9cmSOMLwmYLRx0j01panw4YJ2VhUSqy0m1xEz72063A0lTZ2cS007XdWy2He2mY0q2N3HIgeERM/5sXIUwrsIx+0p3XzE4g6iXLVN+8+sU7e1w1VUOsw8amPyL1hmJyEzgVmAesBP4V+A6Ve22SVVEqoFbgLMAB3gc+L6qbvfJnQn8ApgGfOrmfW9Peu2WM+rogLDbY27zerjhu7BxDXzzMvj6JWYwAEAiBq/dCR89CXX7wnH/YPYekvEmmtY/RPvODwlGxlA17gzCVdOyXjaaamJF7C02JlYSpIR9Sw5iUmhWj04pRYoVbOFNPmMtOwjiMIPRzGYf9qWuz6UlMF+r61LtvJFs5M1EI6tSURQoxeGAQAWzAxUcFKhkohPJS9VZXJV1HcZBrelIsiGWYH0syYZYkvWxBE3JzP+ZsMCoUIBRoQCjQwFGhRx3H2B0iTkfFQpQ6diZFyzZSaSUBreX5LY2pd7t0r/N3Ta3KhubU2xsMU7PSyQIk6sdptQ4TKkRptakjx0qdmMG+m3blOuvS/H556aENHfu7j+7RemMRGQYsBRYBtwITAF+C9ysqtf0kPZpYD/gR0DKTb9FVY/2yBwFvAjcBjwEfBm4HDhFVZ/pLv9+O6M1a+DII+H66+Hb3zYzd7c2w20/h1eehJlz4QcLYIxnLaI1b8BLt0F7M8z+Csw9H0oye6m1NXxI88ZHScYaCFftT+XYUwmVjc2qQlNyOytib7EluYYAQfYJzWDf0GzKneqs8l620MQS1vIRm2gnTgVhZjGWmYxhHDV96oXnpVkTfJhs4YNkM+8nmtmoZobSCA7TAmXMcMrZL2C2weoI0RcaE6lOx7Q+lmRzLMnmeJIt8SSb4ym2xJO0ZGmoKBEzVmp4MODuzdZ13BVeHXCoCgoRsQ7M0oWq0tBBp2Pa2GJm+Vi9M8XqnWbuRO+jN7lamFUXYFad07mNKOv90IuWFuVnP0uxfh38/FqHWbN271ksVmd0FfBjYKKqNrlhPwauBUanw7KkmwcsBo5V1ZfdsMOAN4AvqepzbthCIKSqx3vSPglUqepR3enWb2e0bh1cdBEsWgQnnwy//z1Mn26q6hY9An+6AeIxOOtv4exLu7p/d7TA63fBsmfM1EFzvgYHnAqhrjFJmorTuvVVWjY/j6baCVfNoHzUfEoqpmR9mTUlt7Mm/gEbEytJkaIuMI59gvsxOrhvt2OUwCx1voqtfMBGVrGVFEoFYaYzkumMYiLDCdN/p1GfivFhsoUVqVaWJ1v5LNVGukp+rISZ5ESYHIgw2YkwyYkwQkIF98JuSRqntCWeYnM8ydZ4ku2JFNsTKXa4++0JE+YvaXkJCVQFHKoD4u67HFV1wOmMqww4VDhCecCh3BHKA0K503U8lNWflvzRkVTWNhrntKLBTPL7Ub2ZnirN6HLhwDqH2SPMysezRziM7MZBNTUpV12VYmcD3HSzw6hR/X+WitUZvQx8rqrnecImAGuBM1T1sRzprgcuVdXRvvBPgYdU9XIRCQPNmKq72z0yFwL/DtSqamMu3Xarmi6Vgttvh5/8BNra4IIL4JJLYN482LEV7rrJOKayCjj5G3Ds6TB5hilFbVkJb90N69+DcAVMPxamHg0jpkLAvPxTiSit2xYT3fYKqUQrgZJaIrWHEK6aQah8/C7tSu2pKOsSS9kQX0lUmwgQZHhgHCMC46kLjKPcqcm5dhJAG3E+YSsr2MInbCVGEgHGUM0EatmHYYygglrK+zSoNkNHTbIqGWVFqpVVyShrUm1s1q7RnOUEGO+UMsYJm01KGOOEGSElVEmw4HvJxVWNg4qn2JFMsT2epDGpNCVTNCaNs+o6TtGY6Drv6OW/b1igzHGoCEiGsypzj0tFKHWEiGP26fOwkyWuM4zO84gY2UL/rfdWGju00zF9WJ/ig21JPmnQznaqMeXCgSMcDhoRYPYI46C8JahNm5TLf5hi9Bi48Uan31MJFasz2grcpqrX+sJbgWtV9Tc50t0HjFTV+b7wJwBU9TS3LWopcJyqvuiRORR4EzhMVd/KpduAdGDYuhUWLIA77jBOqbbWzGgYiUBHFLZshJ31gEKwBCJl4ATM4jqppOltl3RfyI5j4kQ6N3NXUyCKppeNE7pkENOalg53zzufBiEzvjNd+rhrr7681BvXmbcnbadsWiYzv04bfGEZco57Xa+8kz5P5+nPx712Z16e6zu7yqrj2bu/s6bzdyRTLv37OY772wkqTqet6gjqAGLyMHLSKYsIGnA6bVKfvhm/c6fejsnbndInrbt683XRdBWqdN1jTd8P73k2pPPPLvjz8ObfGdDTe8vvwDrzyHHNTvnMeE0H7ZJs1/w75XdVxn1mc+jX0+uym/epeKLU/ZtxqWxTPaXzy5WvG+xki9euAyHz4uoV0Mw0/idCPHlPufUZtk0Zz9g/LcquTw9054zyXwGfm2GYTgt+Gty4/qTb1yNDFrkGX3wnInIpcCnAhAkT/NF9Z+RIuOUWuOEGeOghePVVWLXKLPeYTEJlnRn42tIEbVFoipr1kBTzYKYfkFTKDfeEKebh63zr+B7ojLeRZjyMsotMjvPO61iKmr7cwP6WegbrGn1SR7IeDug1dqdU2G3S7M509/Ls5zVaYozY1NKXjHtNITsjyP4dIjnC+5POfy45wlHVO4A7wJSMerh+76mshAsvNNsgMSQOQ9V1jNq1dXeePk6lzJZMGqeayrUlM9Mk0044nVbN6MZkEjRpjv1p0+mTiV3PNQXJtF6ea3XmnczUJ/0BkNYjwx7f9VFfWvXkqW567ZJV9wPBvYZmxJH5G+L9fbXrPOUJ994jc2B2u3SyyCZL1zX9Mmm5jCBfvP8a/nwyvspTOWR9xznT5yhFZJx383GV6zztZHaJ86nUGSDZr5mO61zgPsc1u6O3olnz9LzePKoaWe9bwnPuzyccJvTbW3upRN8oZGfUAFmXJq0me8nHm25ElvAaT7oGT5hfhh7yt2RDpKtbumVAsaVPy97AwE6vPLAsB2Z4A0RkPFDuxvU6ncsMT7rVQDyL3AxMV/CV/dDXYrFYLP2kkJ3RU8DJIuJdwvRcoA14qYd0o91xRACIyFxMe9FTAKraASwCzvGlPRd4rbuedBaLxWIZeArZGd0OdAAPisiJbgeCa4GbvGOMROQTEfm39LmqvgYsBO4Ska+JyFnAfwGvpscYudwAzBeRW0Rkvoj8GjPw9fpBt8xisVgsGRSsM1LVBuAEIAA8BlwH3Az83CcadGW8nIcpPf0ZuAtYAnzVl/+rwNnAiRjndQbwzZ5mX7BYLBbLwFOw44wKmQFd6dVisVj2ErobZ1SwJSOLxWKx7D1YZ2SxWCyWvGOdkcVisVjyjm0z6gcisg0zYWt/qQPqB0idfLKn2AHWlkJlT7FlT7EDds+WiaqabVIC64zygYi8nasRr5jYU+wAa0uhsqfYsqfYAYNni62ms1gsFkvesc7IYrFYLHnHOqP8cEe+FRgg9hQ7wNpSqOwptuwpdsAg2WLbjCwWi8WSd2zJyGKxWCx5xzoji8ViseQd64yGCBGZKSLPi0hURD4XketFpKBXoxORqSLyJxF5X0SSIvJiFhkRkatFZL2ItInIyyJycB7U7RYROUdEHhWRjSLSIiJLROT8LHKXiMgqEWl3ZU7Ih765EJGzRWSxiGx3dVwhIteISIlHpijuiR8RGefeGxWRCk94wdsjIhe5evu3v/PIFLwdACISFJEr3f+DDhHZICI3+2QG3BbrjIYAERkGPIdZz/dMzDIVl2NmIi9kDsAsq7GS3AsOXgn8FLgROB1oAZ4TkdFDomHv+SFGt3/EzNC+CLhbRC5LC4jIeZilS+4CTgWWAo+LyKyhVzcnwzG6fwej45+BfwJu8sgUyz3x8xuMrn6KyZ7jgXme7UFPXLHY8e/A94H/D5yE0bvNJzPwtqiq3QZ5A67CLHVe5Qn7MRD1hhXaBjie4/uBF33xpUAj8DNPWDmwDfhFvvX36VqXJexuYI3nfAXwZ6/9wIfAf+Zb/x5s+yWwE7NCedHcE58NRwM7gB9hPtoqiukZAy7y6p0lvljsOAWzCvbMbmQGxRZbMhoaTgUWqmdRQOAeIAIcmx+VekZVUz2IHAFUAfd50rRi1p86dRBV6zOqmm36kneBkQAisi8wnUxbUsD/UGC2ZGE7kK6mK5p7ksatrr4VU2Pgv09FZ08OisWOi4EXVHVZNzKDYot1RkPDDGC5N0BV12FKRjPyotHAMANIAqt84R9THHYdAaT/6dL6LvfJfAzUikjW+bTyhYgERKRMRI7CVKn8Uc0najHek7/DfG3/c5a4YrNntYgk3La8/+MJLxY7vgisFJE/iEiT28b9oIiM9cgMii3B/ia09IlhmGoUPw1uXLEyDGhR1aQvvAEoE5ESVY3lQa8ecTsmnIn5EoSu++C/Tw2e+G1DoFpvaQXC7vFdwBXucVHdExEZDtwAfEtV4yLiFykWezZh2lDexKw8fT5wu4iUqerNFI8dozFVju9jVsyuBH4NPCQih7sfPINii3VGQ0e20cWSI7yYyGVXrri8IyKTMO1Fj6jqnb5ov86FassRQBlwGPAz4A/A99y4YronvwTeUNUnu5EpeHtUdSGw0BP0lIiEgWtE5HdpsSxJC8oOjD4CnKmq2wFEZBPwEqZzxvOu3IDbYp3R0NAA1GQJryZ7ialYaAAqRSTg+0qqAaKqGs+TXjkRkVrgKWAd8C1PVLoEVINpnMVzDgV2n1T1HffwVRGpB/4iIr+liO6JiByAKZkeIyLp37nM3VeLSJIisicL9wPfACZRPHY0AJ+mHZHLq0AMmIlxRoNii20zGhqW46tLFZHxmB4o/jaKYmI5pkpiqi98lzayQkBEyoDHMY39p7mNrmnS+vrrvGcAO1S1kKro/KQd02SK655MA0LAa5gXXANd7UYbMJ0aismeXCjFY8fHOcIFSHdoGhRbrDMaGp4CThaRSk/YuZi++y/lR6UBYTHQBJyTDnBf+KdjbC4YRCSI6Rk3DThVVbd641X1U8xYKq8tjnteULZk4Uh3v4YiuieYL+7jfNuNbtyXMeOOiskeP1/H9A5cS/HY8TgwW0TqPGHHYD4a3nfPB8eWfPdr3xs2TIPfJuBZ4ETgUswgsYIZX5BD7zLgbHd7DTMINH1e5spchekV+PfACcATmH/AUfnW32fLHZgv1O8Dh/u2sCtzPqaX0DWYF+OdmA+GWfnW32PH05ixOKdiBiRe5z5L93hkiuKe5LDvInzjdYrBHuAB4CfuffkK8B+uHZcVmR1VmCrs1zDO5ZvAeuBZn9yA25J34/eWDVPf+oL7ctuE6UEUyLdePeg8yf2HyrZNcmUEMwPABte2V4A5+dY9iy2f9WSLK3cJ8AnQgan+OiHfuvvsuAH4yHVAO10dLwNCHpmiuCc57MvmjAreHmABZtB01NVxCXCBT6bg7XD1nAo8iemx2YD5KBs22LbYJSQsFovFkndsm5HFYrFY8o51RhaLxWLJO9YZWSwWiyXvWGdksVgslrxjnZHFYrFY8o51RhaLxWLJO9YZWSwWiyXvWGdksVgslrxjnZHF0g9EZJKIqIjcmW9d+oKI3CUiW0WkPN+6+BGRL7i/6bfzrYtl6LHOyLLX474A+7JdlG+d+4OIzMUsm/ErzZyxvCBQ1SXAw8AvRKQi3/pYhhY7HZBlr0dErs0S/H8x6039jl3XMnoYM2nsFKBRVTcNqoIDhIg8g1mMb4yqtuVbn2yIyGHAG8A/qeqCfOtjGTqsM7JYsiAinwETgcmq+ll+tdl9RGQ6Zq2Zf1XVS/OtT3eIyMeYGeP31V2XtrbsodhqOoulH2RrM/KGicgUEblfRLaLSLOIPCMis1y5ESJyh4hsEpF2EXlLRI7r5lpfdPPaLCIxEVkvIn8SkbF9UPlizEzL93ZznaNF5EERWe3qtVVE3hSRrCUUEfm6iDwlIvWuXqtE5GoRCeSQny8i94rIBhHpcO1fKCJn+UTvASZgllux7CVYZ2SxDDyTMFVNozDT7z+DebG+KCLTgNeBQzGO4T7gIOApEZngz0hE/hb4K2adnEXALcDbwHeAt7OlycGJmLWaXs8WKSJXAy8DX8AsLX0T8BgQBk7xyQZE5L8xy2pPxSxaeBtmJdBfAn/Okv8trv7HA8+5+S9yr3eET/yv7v5LvbTNsieQ77Uz7Ga3QtzoWv9oUo74SW78nVnCFNPm4ZX/qRu+A7gdcDxxF7hxN/vSTAdimPWVxvnijsc4l4d6YUs5kAA+zBE/yo1/BSjJEl/nO/+Dq+//A4Ke8BDGkSgw0xO+wA27Hyj35VUBTPSFVbvyb+b7ObDb0G22ZGSxDDyfAb/yhf3F3YeBK1Q15Ym7G+MMDval+S7mBf8DVd3ojVDVF4BHgdN9y9lnYxwQwCzqmI0ZbvxKVY35I1W1Pn0sIl8Evgc8oqpXqWrCIxf32PlFV34OZgXUt4Fvqq8Xn6q2qOpaX1gj0I6pqrPsJQTzrYDFsgfynu7a8P65u1+pqs3eCFVNisgWYB9fmnnu/lgROTTLdUZinMh0zMqiuRju7htyxC8FGoGLRWQE8F/AM6qaTf4yTNtTNEcvxFnuXtz9DzHNAVdmc3TdsANTYrPsJVhnZLEMPI3+AFVNiEjWOJcEphTkJe1Erujhej2NyUl34y7NFqmq9SJyFPBz4MvA6UBSRJ7FVDe+4xE/yd2f38M117n7kzFOcFEP8n4iHr0tewHWGVkshUvacVWratNu5LPV3Q/PJaCqHwHniEgJcAxwKXAOcKiIjFPVDhEpBUYAL6vqsT1d1CP/nq9asqd0DlADrOltGkvxY9uMLJbCJd3z7ejdzGcTsA3YrydBVY2p6nOq+g3gVYwDS1eXpave6np53bT8yD7oCkZPAd7rYzpLEWOdkcVSuPwBiAM3u4NWMxCREhHp0VGpqmK6bdeJyFRfHnNEZEqWvKdi2n/WARvcfNqAD4CZIvK1bNcSkaPS44xc+Y+AsSLyjSyy03OMSTrc3fe1as9SxNhqOoulQFHV5SJyMWbczlIReRpYiWlbmoApMW3D9IbriQeAr2PacD7xhH8f+BsReRPTkWErMBk4w42/2FfFdgXwBPCAiDyHcU4OpsfeF4CQqnp7wV2J6fV3j4j8jXuNGkzPwfGqOiaLridhuq0/0gu7LHsI1hlZLAWMqv6niLwPXA4ch3lRt2J6591PNzMq+HgA2AJcCPyzJ/wRzHvgMEwbUamb993Ajaq6yqfPMyJyBKa79lHAfEzb1ibMYNb7fPJPiMh8jFOa5+pfD3yImfcvAxGpBs4CHlfV9b20zbIHYOems1j2EkTkKswA1ENU9d1865MNEbkM+D1wjKq+km99LEOHdUYWy16C27ttBfCBqp6eb338iEgEWA0sVtWz862PZWixHRgslr0EVW3HTD30diEuroeZTukO4Ed51sOSB2zJyGKxWCx5x5aMLBaLxZJ3rDOyWCwWS96xzshisVgsecc6I4vFYrHkHeuMLBaLxZJ3rDOyWCwWS975XzqVvESHcvz7AAAAAElFTkSuQmCC\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Simulation\nNext, we simulate sample paths and the trader's optimal behaviour along those paths. To this we\n* obtain the optimal limit order price for the current inventory and post it\n* check whether we are behind schedule ($t>\\tau_q$) and if so execute a market order, and cancel the limit order\n* step forward in time\n * update the price\n * check whether an incoming market order arrives\n * if a market order arrives, check if your limit order is filled\n * update cash and inventory"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "In this simulation, we use the parameters\n\n\\begin{equation}\nt = 60 sec\n\\quad \n\\lambda = 50 / min\n\\quad\n\\kappa = 100\n\\quad \n\\sigma = 0.01\n\\quad\n\\alpha = 0.001\n\\quad\n\\xi = 0.01\n\\end{equation}"
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "np.random.seed(30)\n\n# Number of Simulations\nNsims = 1000\n\n# The Mid-price to start with\ns0 = 1\n\ndeltaPath, Qpath, isMO, Xpath, Spath, pricePerShare, twap = lth.generate_simulations(Nsims, s0, Ndt, Nq, dt, delta, lamb, kappa, sigma, xi, t_opt, t)\n\n# Choose the three simulation results\nidx_fig = np.array([382, 57, 1])",
"execution_count": 7,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Depth vs Time (sec) of the simulations."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_multi_lines(t, deltaPath[idx_fig, :], r'Time ($sec$)', r'Depth ($\\delta^*_t$)', r'Optimal Depth Sample Paths')",
"execution_count": 8,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Intensity vs Time (sec) of the simulations."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "intensity = lamb * np.exp(-kappa * deltaPath[idx_fig, :])\n\nlth.plot_multi_lines(t, intensity, r'Time ($sec$)', r'Intensity ($e^{-\\kappa\\delta_t^*}$)', r'Corresponding Fill intensity')",
"execution_count": 9,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Inventory vs Time (sec) of the simulations. The blue dots indicates whether it is a market order."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_inventory(isMO[idx_fig, :], Qpath[idx_fig, :], t)",
"execution_count": 10,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Cash vs Time (sec) of the simulations."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_multi_steps(t, Xpath[idx_fig, :], r'Time ($sec$)', r'Cash ($X^*_t$)',r'Cash Sample Paths')",
"execution_count": 11,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_multi_steps(t, Xpath[idx_fig, :]+Qpath[idx_fig,:] * Spath[idx_fig,:], r'Time ($sec$)', r'Book Value ($X^*_t+Q^*_tS_t$)',r'Book Value Sample Paths')",
"execution_count": 12,
"outputs": [
{
"data": {
"image/png": 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LzCvbJCJTiIfgcDgcDkcVUakCSVUvBhCRjZgwLJ0wScR2BA6x16vsKMd9McELpwfKp5JlKBQRKcAkSXu2cobmcDgcjkzJ1RpSY1UtwYSzGJGja3i0BNbYGY+fIqCRiDRQ1U0Z9nW57e+xqAoicgZwBkDXrs7P1+FwOCqLnET7tsKoKgmzXZcU55IrixyCEUj/VtVfIy+k+oiqDlDVAW3bJhmJOBwOh6OcZCWQROR8EfndRmWOqtMy6lyOKAKahoTybwGsU9XidB3YFNAvAw+r6t05GKPD4XA40pDtDGkvjJVbUsQGETlVRIqApSKyREQuy0VCqhB+wYRf7x0o72vPpUREtgTew4SIP6fSR+dwOByOjMhWIG2DcUxNyPwpIjsCj2DyzAsm5/31wP8qY5Bp+AoTAn64bzyNMGmoP0jVUEQ6YtIOzMSkVQiuQzkcjtrAs8/CmpRplBy1gGwFUntgRkj53zGC6BlMWoqBwGTgnzYTZLkRkUYicqSIHIlJ5NXWOxaRRqq6AZNr5DIR+aeI7IvJh5IH3Ovr50QRKfGycdpMmx9gjBhuALa3WTgHishOFRmzw+GoQl55BU48EZo2DT+vCl9/DQuy8jhxVAPZWtk1wCTBCnIQJvHU+Xb29IfN6PgrJsHWNxUYYzuMgPHjHffAOMDeghFAl2JmZ+Mxief8WVDzMKo9T43YHtjB7gctAefgAsE6HLWDS3yeJOvXw8qV0KFDvGzKFNh9d7jlFvj3v5PbO2oM2QqkhUA3f4GIdMbMisb6VXmq+puIfIJJrVtuVHU2cSESVUeBG+0rqs5TmOyaGffrcDhqAXN8UWgaNTJbf9DotWvNtmPHqhuTo1xkq7IbBxwkIv658TC7/SKk/jSgS3kG5nA4HOUmbD3JuWnUeLIVSI8ATYGnRaStNfH+J8bX56OQ+mvKcQ2Hw+HIjJIIl8e5c6t2HI5KISthoaqjMFEMDseo75ZiwgLNVNWxIU22ABaFlDscDkfF+NOfoH59s3/66YnngseOWkF5Zi//AK7BOKQKMA84MaLunsDv5RqZw+FwpOK99+L7AwbAZ5/Fj7/8EqZOrfoxOSpE1gJJVctU9TpVbQO0UNWuqvp1sJ41v+4KjKr4MB0Oh8PH8uWJxw0awNChicYM/fpBWbpkAY6aRIXWd1R1VYrTHTHCKNfBVR0OR13j008Tjw85JL5/113x/aefrprxOCqFnBkcqOpzqrpPpunAHQ6HIyPWrIHffksoWrK0Ld89aA9OOSV+4p//hEV2GVszirPsqEacBZzD4ag9vP66icjwxhvmeOFCUOWLa+H9s2ydpk3haJsKbf16eP55s9+kSZUP15EdTiA5HHWRWbNABEaMgNWrq3s0mXP77Wb77bdm284kdy7dBK288Moi8NJL8TY//2y2Ln9ZjScjgSQig0Wki93vJCKDczssh8ORM446Cnr2NPuHHgrNmsHixdU7pkz5xheFrEEDI3wALYP6jQN1H3/cbH/6yWydY2yNJ9MZUgPgTrt/J1A/N8NxOBw559VgaEjiKrDaxKZ4Imgti8mmOMcfn3jshRVy1FgyEkiq+jmwWERuBJZZB1mHw1Hb8FReQc48M+SOXkWsXl1xgwMFCd7NCgoSj6vr/TkyJq1AEpHPReQzTEqJS4FdfWUOh6M24Y+MHYY/UGkuKClJ9A367DOjMszLg1/S5NNMke9Iy0IEEpg1MketIa1AUtWhqroP8DUmzcO3vjJHTUDEPf05sueLL8zMxD9r+qYimWIyoH59yM83+/fdB/vuGz+39dZJ5twJBH2PbrghthspkAYNKv9YHVVOpkYNewPtVPUyoLU9zqTdZBFpXv7hORyOSsOvFvv6a9hzT7N/0UXmGGDZstxd3x/ap6QEzjknuc4PP8CKFcnlAOvWme2f/wzA4ka7sMlOmmZ8CPO+DWnTsiXcemvc0s5Ro8nUqKEEuNDuXwhkmup7G6AgWCgizUXk/gz7cESxdKmJ2eXx2mvVNxZHzaeoyGzz8mC3QCLnLbc02xlhCaEriVmz4vurIoK8DB9uhMjGjcnnli412wsu4OcHF/HgBQfwyX8yuO4ll5jZl6PGk6lRw1hVnWv356nqmFT1ReR9EbkGk5Zii5AqjTBpzx0VYeBAGDIkfjx8ePWNxVG1XHYZnHVWXF37dVI4yWSee85s//nP5HNe+u9x4xKKF06EJZU1uWjYML7/+uvx/ZUrk+suCkkS8PDDZtumDa+eafyPvrsfvoyw03DUPrLNGJspU4C9MdHAvxWR1cBEYAIwCegLuAT3FWXmzMTjLcJkv2OzYvFiaN8+uXz33eHjj+Hll+HeexNv/h7f2SheBx+cfK6evRWMG2fSOlhjgId3NMWXLIPCVhUc+yuvxPfPOMNsBw82Rg2qieug3bqZ9+r3HRo2DKZMQbdKnO18Yu00dvhbBcfnqHZyIpBU9WIAEdkI7A50wuRN2hE4xF43jbmPI2vOPbe6R+DIFWvXGv+hk0+OrrP//mbbowe0aRO/6YPx2fFmSP36pb7We+/BrFlM+7lHrOihHeFfFU0k8847yWW33hrfX7vWGDl4s71PP4VjjjH7555rBC3w2+fhip2t/1LB8TmqHdEcBhwUkXqqGpHSsfYzYMAAHT9+fPUNIGhZd+aZ8MAD1TMWR/koK4MNG9I7be6+e2ZqOT8zZkCvXmbf/1spLTXrSEEeesj8hizXknhvuLqit4owS9D16xNncxMmQP/+8WPv/uRr641rzyth9PWVOD5HlSEi36vqgGB5TmPZbc7CqEbS3Bk01jp69YLGjWGvvcLP//YbXHpp9sIITBqG0oD90aOPhgsjgH/8I2V3S1O4CWX8XFs/EOQlqFrcccfEY88Qw/It8fWvbY6Cv7yY4XUdtYJyCSQR2UFEnhSRX0Rkod2+KCLDRSS/sgfpyJASJ/9rHbNnm+3o0cnCY+ZMI7BuuSW53aOPmu311ydaWvq5/36zNrRggYl03b8/nHZaRsPaRDAwHKxZmFyvZAO8ciRcl+pO8uKL8ZTiF14Yt7a74orkuiJw003xcex/ODf5gnSP4trYfustYdtj4OSxcGm0z6yjFpG1QBKRk4HvMGnLtwTa2e3RwEvAFBHZs7IGKCK9ReRhEZkoIqUiMiqkjojIZSIyV0TWi8hoEdkxpLtgu/2tIJ0tImotA2svwRuao3ZRL7Ck27t3eD0wOX8+/BAuv9w4f6byH+rUyUQ56Ns3/RisoYwQj6Zw/Adm+/RQ2LQ2sfqNhTDVGswtnBjS34gRcNxx8Nhj5rh5c+je3Uyprr8+pAFmRrjTTgA0+H60WVsCvud01tM6Vi2/gdl2HQwNkuWnoxaSlUASke0Ba3vJfcCfgB2AfYDLgJ8xwukTEcnsUSw92wAHA9PsK4z/AFcCtwKHAmvsGDqk6ftAYHvgU2BdpYy2Ovnqq/R1fvvNLFo7qp8ff0wuKy42W38GVD/jxpl1p7w8Y3Xmra20amVmQiUl8VlXkB49wsv99OzJup32pYx8WvWBq8qg6x7x00/4Ah/M+jyx6YpZJPPgg4nHHTumHwPAxLh0a4KZmi1kR86bBceOgGPezqwbR+0iWyu7f2GE2P424KqfUcAtInI88ADwkIgsUNWK3v3eVdW3AUTkNaCN/6SINMQIpJtV9T5bNg6YDZwNhOgFYlysqhfaNodVcJzVTyZhX7bf3jxxuuyZ1U9YRIIGDcLrvv8+HHRQ6v462Oevbt3Cz0+Lep5LZGOv/rSc8CmHP1GGSF7C7GPRpPj+M4HgYSXWl3XdMpj+TjHbt/oAef/9xEobNmQ0Bs47L5aK/EDOA2Cfk2ZS2B1adM+sC0ftI1uV3d7AyBBhFENVnwd2AYqAR0SkCYCInCUiF0a1S9FfWZoqg4BmQMzJQVXXAu8CKf/BGfRde2jSBA4/PHWdqVNj6g8mTIBnn839uDZ37rgD3nqrfOt3njNqKlNugPnz0wujIOPGof13puiG5+JlUSqyAPlFxim19ZVxR+s+PtclLUueHQH8bP+B754OO5zSADk8/oxXdu0NxhT9qKMyG/+dd8Z2t8Q80xYOykDl6KjVZCuQOgIheoZEVHUacLKtf4WIfAjcCyErpRWnLyaU0fRA+VR7rm6QiTrG73/Svz+ceGLuxlNXuOgi+L//g/PPz6z+nXfCSSeZGao3Sz3iCPjjj/D6p56auZrLz8CBfHPieO65wpcTaKutMmq6dksT/aPRqDfMA8zNN3Psq+tpbIIj8N0DibOjq+xj3dQ3YObHMO3NTQR5+6cLYckSExYoQxawU2JBhgYZjtpLtgJpLRkKFVUdgVlTuhg4ABgH5OKRvCWwRlWDK/pFQCMRidCBlA8ROUNExovI+CVLllRm1xUjP98ZNVQ13noPGIu2dDRsaKzMnn7arAF5KrS8POjc2RgpHHlkvL6IEXjloLQYPrIy8lqUopmZKwPeHH16/KBJE7jsMqRxI9rYx7sPAjFR/e5Fkw94miuTw1cy6dVE8+5538Frx8D6IljwQ/g4RvLf+MF117mI9nWAbAXSHGDbLOp79qgXAnuoatiyZ2UQtiAiKc6V/0Kqj6jqAFUd0LYmpUTOz4dff82+3YQJ5WvnSF4DEkm9RhIMGOplNJ03z2yHDTPRGHbaCYYONcYLmVjGhTDl5cTj8Q9lfjPvsAM8T/LSb/ehcC49uJAOCEZFeU4gFmt/Ho3tP8973Mha/mujhE33LSe9daIZ422t4JGd4aML4YfH4VqB984y2+X0iTe48sqMx++ovWQrkD4E9hKRXhnWXwKUqupdmruQEEVA0xD/pxbAOlUtDmlT+ykOvK358+NrEkFSzZz69y/3Ta/O065dcllhYfb9BAOJfvmlmS2lYP735qb91knh5xsEfgpf3Q6rM4weWdga5jI4qXzT70tpyWyasIjDOAWAVoE7QWfiOSBmcDAlNGItxtjiBZ/hYNDJ9us74V2rkRtvDfPW04riBs3jJuOOzZ5sBdJjQDHwfIaqsK5ADhOsAPALkA8EnTb62nObP2vWwA47xBOf+Vm+3Ph+PP546j68p3RHxVmXpQfBrrsmHhcWRlvbWR61QVcmPm0E0yrf1zfzY3g5xL5l/EPph1I0C769FzbSPDGzK9CjWzyYbxn12N3TJpaVcfV/7+CklxeST+rnvzE3pTydQDGNeWH35WYdzVEnyEogqepvwE3ArsAYEekaVVdEOgKHYZxoc8lXwCogZhIkIo0w/kgf5Pja1Ydfn964sREoP4Qo4+fPNwvT6RaEw6IBOFJzxBHh5atXJ5elUhAccEDGl1SFhSFmRT/ENWU85+tuyz/F9zdE5L3zWF8E9/T0FYgYnyZr/NK11dTYqZ14kgO8tA9vvQUXXUS3ozvGYueVzvidgRfAmZPhfF9Q1s8uh19DYqxGsf2JOY1u5qhhZP1tq+r1wNMY0+6pInKHiPQXMQmERaShiBwKjAaagE+pXA5EpJGIHCkiRwKdgbbesYg0UtUNmNTql4nIP0VkX+BV+97u9fVzooiUiEg3X1k3X98NgH72OEsb2xrA5MnJpsdlZXD00Zm1z2RR3pHIG2+El3foYMLl+PEMYC69FO65J6Puv/ovTHo+sWzOF/DwTsl119ruXzsmsfzYd+P7jUM0jH7uCHMj79YtNoMrONdnnl7gM1zwqxdtpIf8Xlsw7A5oty003wJ6+DKVv+Tz+Gu/feoxbZGsOXRsxpQr/YSqniwivwLXAOfbV4nNe9QCY1AgwFOq+m5kR5nRDiNg/HjHPTAOsLdgBNClQGtgPMZ516+cz8Oo9vyru0OBJ33Hw+1rDtC9guOuHMrKzAzo7rvh7yE5DTt3jm67ZEnmqZuHDSvf+Bwm8OmsWXDssfGyjz9OPPZSQSxfDj17kgkfX2y22/sstzdGJFpdPQ9Wzk02ZgDY9xb49D9GMESxcRWU+qy1m/t9a7t0SW7Qo4dxxO7bN55nKQWzPk0u630QHO8zdNiwEho2NypIgM67mXh1jrpDuefDqnoL0AczC/kdqA+0sn3OBs5T1VMqOkBVna2qEvGabeuoqt6oql1UtVBV91DVCYF+nvK3CZQFX90rOu5Ko7jYWG5F5TryIjSfcw60aJF4rkO6yEk+XCPbeLkAACAASURBVHK/7PCr4HbbLXkm+tZbiWFzPMOFYcMy8hmL0vDl+R4hD/XpHtYshJERbueeQEsVrfvTyxOPz/F79XUN0cz/8ks8Y3HQ2jREdTzgrOQuegf0EA1tsPrTv4OzfobTvnaW3nWNCiloVXWuqp6vqj0wM5OtgA6q2ktV703T3JEJ3j8ysMCcZDmXn59cJxvK43xZl5kV8GAQgc994QuKikyKcS++oDeT3XPPxLvs0KEJ3Sz9FR7cDn77OF52rcAyKyCKfouX9/ctC877Bn4O6BGOtJETGtsEs2sXR7+d7+7z9XsG5PuzROwU0BH6rTl/+in5QShYHzj4Pjh1HLTyWXK3iTDu7DQA2m4dfs6xeVNpK4aqWqSq01U1xc/ekTWexVZwfcjzgVlj4+7n5WXuGDttmnmy9ROMNO1IjSdo/DmEttsuuZ5nnv+6DYldUGCCoHoEYr09OgAW/wTPBTSoY24020WTzdYzFDg7woXsosWwjTXz8YTLhDSGlh55YQlkli+HffaB116DZ55JPPeqlYRlZcm+VhYR6DIQDrMK8pa9oOe+oVUddRhnwlLT8f7gwZAr3o3Oywi6aVM8Tl0qfvoJ+vRJ9lnK1lS5rnPSSWbrnx00a5Zcb6FNIuTNQJs0iZt5n3VWUoK6TRF5fSY+bazgfnjEHNezzVpvmaz6umIjNI7w2Y6KiuCnadiyZMuWJqX4X/5iYtKFIZLWXL3rYLhsLZw7A8TdfRwB3E+ipuOp4YqK4Np4cjK+/95sPUuv+6zOZeXK1P1ts43ZBs2809xIHD6mTYvPRv0BS8P8wFatMt/bggXxGVSfPub7vO++5Pop8Kvk6vnkWNfAZDc/5Kvsb20q1ixKPlcWmHx3TWfZFvY+L8w8bnL9NNnaHXUXJ5BqOv51oWuuie//YleovZw63pN6plGngwvVLg5e5viDlPpVnWGpwc84I/69+c+3aBG6Yt8nIg0SQDOf3UmBb4JblEFArp2sedEHZyefu96q9HofCP9eAd33TtPZ7rsbIxu/6vGUCtsvORxOINV4ogwVBtlMaQ9Z9/urrjLbsKfXMII3z++/TxuuxmFplMEj/lkhZmUZ3LSTQgT7KA1fnqFRhAbNTysbx8RvFKFq4sZ5tNk6bumWlv/9z1hxTp5srAn9keQdjnLiBFJNJ8r+15vRNLd3EM+seHowC0cEQYH04YfZ59ypq3jrbXvskXxu6lRYujSWXC6B1q2Ty3yowozAM8Fp8dBwfGUjI5w6LrHOUJ8m9x9hacSBRr5Lz7X2GMumxePGAex/W8rhhbPttomGHQ5HBag0gSQiT4jInyurP4claobkqea8GZEXGeCKkAS5m5Lz09CkSbjDoyNzRo9OLuvb1wieBg2ShX4aS8a5vgz0hzwI//oDOu+SfD4/kN0hvwFsewxsfUT6yAcATww2gu+RnRPL85yhpaOaqcwZ0knAjpXYnwOiBVIwoZsnmNq3T65bv35yGcDcuckzsE2b4L33YMcdy5cFta5wWAYZ74NrRI3TpBLzfRUD/gHNrLXbfwLRGcJUdEe8AMNfSz8kj+cPgmKfUWbXkMmew1HVOJVdTSdojv2//5mtJ2Q8YwZPsJSVmRxHniDLNJOpx7vvmkCsEyfG46854jz1lNlm4oQcFPZpnI9L7BpRYUCzVxCw0A+byYhULKrB0MyymzscOcUJpGpgBeu4jveYSgYJaoLx6zwB460heQvsnnro+edNjqNXrJt+0Is+HYsXx4VdmKqvLrNgAZxsA4yG5UIK0qpV4nHvYIaURJbbZHfHvJ262/Kq1hqHTJ4Bjh0B3fcqX58OR2XiBFI1sAiTnmAif6SpSTwiQBBPIHmqun//O/G8F9jzzjvN9r33YOTI9Ndr29ao8iB8jaQuc7Iv2nVYiokgwViCzVObsH1hjRPCLN08PyIovx/PKV/CsBBbiy1TmJo7HFVJuQSSiOwZfNlT3VOcc1jKMOqe0opkVw8KpD0jPuZVdgHi4INh//3T9+uP4HDiiSZkjMPw0UfxfW8GmgrPaOTxxzOaba6xE+agyg5g59Pj+w3SLEVF0aoXDDwfuvlmQ5dGRIZwOKqD8s6QRgGfB14AfwuUjfKdc1jKrCCayRKe4evUlaN8Xs62Ho6eQKqssMirViWaJ8+YUTn9bm4cfHD6Op5RiEi0YYmPljYrRdOQpabKtIA78iWzPfyZ8gs3hyMXlPdnfnLgWIAngLfty5GCQuKxXWany/B+3nlw882JZaWl8Rh3nsCK8lcaPjy8PIqjjkpcfK9IBPHNmYcfTl/HmxUVFKSuZ2nWJdFx1U9lCqQmHeDqCkzOHY5cUd4EfU8Hy0TkCeDHsHOOChAIvgkkrl94AT2jQv+8HJKxLay/11+PBwz1h4R55hmT98Zh1td23hk++CCz+l54pgyF+oo5JiJ2GAUhcVsdjs0NZ9RQ0wm7mY3zuep71nVh9fLyMlPlNWkC20d4VEatTdU1VI0ZfJ8+6et6nH02bLkl7JWZCVtBU1i3NPxcM+fD7KgDON/sakADxgzfPQjtt0uO2gyEz3yWhty1OnVKLgsL9hlFVN01btUbiKvfsknTsdtu8GtEwqIQykqgQ3JuO8CkauhzMBSvz/zyDkdtw82QqoGg+v79s+DZA+zBokWJs53gzGeffYz1W5DWrZMTxGUaaBWiZ1LZ9LE54wmkvhFpTivI+uUmxXhY6giPY96BEzKw3Hc4aiuVKZDmACsqsb/NluUkJ9IrWY/JkdOhg4nc/dNP5oRfIPXvn3o9YvLkxONsZkhRAslLBFjXefNNs83AWq48vPFXs536RnSdvHwXb86xeVOZKcx7qOo9ldXf5syHTAk/4fkM3Xijme1MmhR3UgU21ROKylKo0Pr3TzxeXwn6nZkzK97H5sDf/ma2y9JYRZaTGdZOolWvnHTvcNQKnMquGmhH0/ATwVnK3LkJZcvrbWR1WYo1jD/9qfyDilLNZZL7Z3Nnoi+nw9khGe4qyOQX4vuLf6r07h2OWoMTSNXAlkQEFQv6Er3/Pjz3XOyw8PeFdB37c3THF1wQDxUU1j3Kg3zBz2Ex9KIiCTg/JLjuuvh+YWGld//G8fH9IzOw0nc4NldqvEASkd4i8rCITBSRUhEZFVJHROQyEZkrIutFZLSIZJQKQ0QOE5HJIrJBRH4WkaMr/U0ECFrZxQha1D3wQMJh8z8ibIJjFZrDv/4VebqUMpawhtf4Iflk0CDiqKPM7KwuCKQff4TLL4d77oGrr04+/4ZvYaeS15DKAl/5NkdVavcOR62iNiyRbgMcDHwNRNkg/Qe4ErgY+AW4APhERLZV1YVRHYvIEOB14AHgXHudF0WkSFVzZs8U6SSf6uZfv36ygcH335d7DA8zhtMYTL73TJKfD19+CYMHm+NevUxZXRBIOwVsra+5xgjjZcsSDUPq1Qt3VK4Asz6N73cfWqldOxy1jho/QwLeVdUtVHU4JFsDiEhDjEC6WVXvU9VPgOGY+346hf+VwGhVPVdVP1fVi4EPgasq9y0kUrqhhMKlK5PK18yPvvmXrQmJLh1Mb5CCMpSnfXHzFrGKTQQS8A0aFN+/+WYTi+2mm2JFU5jP98zJ+Jq1Fi9yeps2iZ/xqlXh9SuA2KW77Y6HEz9NXdfh2Nyp8QJJVdM9og8CmgGx8MuquhZ4FzgoqpGIFABD/e0sLwG7i0jqXAEVoPcVd3Nx2+OThNL4W5OFlMeMBiEW9Vmoj9aykXkBq/yyLKONv84E3uMnylAWsjJa9Vjbuf12uOOOxLLjjsvJ+tECqz3td2Tlxcd1OGorNV4gZUBfoBSYHiifas9F0Quoj1HxBdvlAVtW1gCTLnzH4wA0XpwogBo22hjZZiMlPPZN4CbZuXN45ZBwP2HCowxlPcUU4bPcC8tqWlzMl8TNvycwl0cYyxxqaWqKZcvSp9W46KLE4y65id3zySVmW69yNYEOR61kcxBILYE1qhqMsVMENBKRqHWnlnYbnHoUBc4nICJniMh4ERm/pIIpvvOLE1Vm+fkRAVKBEkpZ1aVNvGC//aI77pXszBI2G/qFhdzFJ9zrzxDiBWtt2zZeVlrK18TDUI9iGgC/kcbIoiby+ONGFeel2Pjww8zatQz9OVQanXfNafcOR60gI4EkIoNFpIvd7yQig3M7rKwJ0x1JinOp2qZsp6qPqOoAVR3Q1n/TzoLSfPM43P7HWaZgO7M2sXZeuEAqKSyggPqob4H990YbGEtErqKbboIzzoA/4hlpNwTXizCzrhICGlEvzfa118bLysrixg8Y9R/AGjaEX78GMIX5TGNR8onTTks8LipKrhNGvdza/xRmvhzocGy2ZDpDagB4Di53YlRdNYUioKmIBD07WwDrVDUq9k2Rr16wHeQwDNLCPkcCkGfNvLe++hbObtKLvE3hURhKGhfShAI0L77I0PWdsXxGRODODh1Mvh6fSq+EZGHXkhCn14svhu7d4Zhj4mVlZaEzrJo8Q3qdCbzE+NSVRMzakJ+ttgqvm+lMyuFwlJuMBJKqfg4sFpEbgWWqOiqno8qOX4B8oHegvC/J60N+ZgLFJK8z9QXKwOqlcsDCfsYTcnEjc/Pb/+InaL3mN/pNuzG0fsOlK1jNhgSBlC1hAkUI6W+vvWDWrEQVVWkpPWmTVHVVDZ4hlZuRAWt/LxfUmWdW+qVWzzfb7f9a6V07HLWStAJJRD4Xkc+AgcClwK6+sprAV8AqjKk3ACLSCDgUiMykpqobMenVgylVjwbGqWq0yVsF2bjWfOzyubnpe8YNbVZ8G1r/6VE3G9Wazwxr/s5B+Zua0qBqjhQOuh5HmpkcZWVMYl5W16u1dOpkEhXuv79J3z5ypElyeMQRlX6pYmtL0nP/Su/a4aiVpFWMq+pQABG5DxgJNFfVf+Z6YB5WuBxsDzsDzUTE3il5X1XXicgtwJUiUkTcMTYPuNfXz4mYNOu9VNVzprkeGCUidwNv2escDByYy/c046M8BgFinU4brE0905iz13aUMCdhDamkMEWeghBW+2Yzf2cPHmZMeqPtPfeE116rdudYRVnGWtrQJHcX8azq6tWDJ59MPHdUbsInvHOq2c76DHYIySjicNQ1MlqpFZG9gXaqeraIvCQie2eithORycCQCs422gGvBsq84x7AbOAWjAC6FGgNjAf2V1X/qnYeRrUXm2ao6lgr3G4AzgRmAcflMkoDgNqJqRSW0HB5iMNrCPNYQYFPZffJrSdnfL11bGIq8YAVefYj8M+QyigjLzhh9lKlFxWZTzWEItaFr0VVIqOYxhhmcBK705XsVv9/ZRFbRcUO9LjmmvCQQTlmzmiz7dg/dT2Ho66QqVFDCXCh3b8QQlbIw9kGKAgWikhzEbk/kw5UdbaqSsRrtq2jqnqjqnZR1UJV3UNVJwT6ecrfxlf+lqpuq6oFqtpXVV/K8L2Vm5hAmteAJgsztPKC2BrSgp168cegrdNcQ5nMPDZQzAgm86vP4kxCBNKvYRZp1iiiqDQ6QkFkKo1KZDFGMK4gi2ytltkE0kU0b57oa3XRRdUijPzsmPmzhcOxWZOpUcNYVZ1r9+ep6phU9UXkfRG5BmM6vUVIlUbA37Mc62ZDTCBpGWX1w9M+fHLrSaxvmaii2tS0EZ/deCJvPRMPoBq1DjSPFbzJj3zBdH4hMZyfN8/yGzrkhRk4NDBqwbcXf0wh9WlN46Qq5RES2eKNcgOZJQtcRtxa8RtmJZ5cuRJa+Awro6zqckTxOpj8Ikx7DwpbQ/NuUBCRjcThqGvkyrliCrA35t73rYisBiYCE4BJGEu2kBwIdYNmXQT+gLymGyO9pJb37sTdc5+KrTN5jL0scT1jHivoEuLDu9H6HXmzC4+D2CbmU+QXZg1S/BRO2vM/vPTWFUw7bGDSuSWkSBhYSXgx95JUihG8R0RSofnWrG3qVCOIfv3VWBRWIbe3g2JfwuD1ucn353DUSnISqUFVL1bVvTFm1bsAfwU+Brpg1nmGA5fk4tq1gW2GGyHTfP0fSDAHkmVNx5YUN27Ipqap12dWR5hee70G5z270D2mslvqS6UeGtfON7ZjDr8hZtzQlibsRo+U46pMPEfc9UTkbPKhaLKazsOfQfdX68M1alQFR5cdxcnZ6x0OhyXXoYMaq+oPqjpCVW9Q1SNVtY9Nd/5ijq9dY+n79w4AFDdoiJSFC6TiQrP0NpjEMECNA0ty+eX4CgvsbGicLxzQSkLSnY8YkXC445Of8DcG8jd2Z2/6ZH3divJ5Bq5hU0Im3mWeybs323zgAdh3X7P/wgtJ9auSI56v1ss7HDWKrO5mIvKISOYxiVU1OV6NIxalO6+kNDlLLDDppn+yaPvuAOxD4hrHGQxJOI5StRWHhAryCPsCg4JtNRuYsea3hLI/n3YP3WhNIxokXDfbqOHZkhTeKIIRTOYNJiSV/+IZbHj5pFq1gsceMwn5unatrGGmZX2I/Urf/6uyyzscNZ5sH69PA960OYgc5SXfGDLk1S9OWiMC6HTpLbHEcMFoCk1J/OijhIEXwdtTdwExowRPmPh7DhpHzGQJo64MSZ47c2bSuBaSMx/ipLGlutYP/B5aHhOet91mttOnm/BI55xTZTkfitfBbSEW6y7Kt8MRJ1uB9AbwZ0w21rThj0WkQETOLdfINmdsoM4WM5aQX5xsQe85gIZavgWIsrIrtOEGG/mS7HrhfwShDY0TWgbDADWhgJKGIc63jz8eMobcssKnTnyEsVm3X+2195Lt7bxzZQwrK0b4bEq77QUnfAJ/fsLlQHI4/GQrkIZj0n0PAsaKSJhJNyLSUETOxzia3lWxIW6G2DhxA79/kkG3vpZw6vch/QC4ikO4IhagwrBHUri+9PHkvJlMPnnsR9x3yW/QAPGUEh7FlFKWH/Lz+OabyGvkgnUhhgw/MT+pbEnAmrADzWL7Meu8Pnbdq3/Ve6JOei6+32kX6Lkv7OT8jxyOBLISSNYB9WxM6u+tga9EZFvvvIgUisgFGEF0ByaT652hndVlCoxhQkHxWlrOijukLtyhB0+NuS2p+gnsxukMYahdTzqanemNSX2RHyEMvFmLF5F7GP2oT7jPUxh5CKUFIUHdP4uHMPwT2wHwSw4t+GeFRBR/gwn8QeKCzIOMTjg+id05HpNkqJ73My+x62o5TiWRjt3OqdbLOxw1lnJZ2anqjcCpQHtgtIgcLCIXYQTR7UBTjEDqoaoXV9ZgNxt8Mek6fxufmcjaAg5nh6TqPWhDR+IZ1beiAwdhngOi1GVBVV62s5gJzKWkYeosI56wGOvLJluZbKSY10OMFAC+4rfQco8G1KMFJuX4Mm82OM1+1vmZC+Zc0Lzq7CgcjlpFuc2+VfVJ4HhM/qB3gVuBxhhB1F1VL1HViqVU3VyJWDgondGIdf/LLFV2PIugxrazWBrLe5Rs7JB6padTIC3UEtZQb31cXTbrpguDTdgzx6bfa3wGGf3oyJa0ix038xl3TAlR4QE0sibyMaOGpjYkQvPmofVzhT/N1VaHVemlHY5aRbkEkog0EpGLgfu8Iru9xQqimpu5rQbTiR/46PzM6sbj0Rmms5hn+SZmaRYUP8FYdX18N3eA+YF8hFvRPiG6+Jodg2mjoC3mBt8kOVxhpeAXSPuwFcOJGyMUrC+GG26ASZOYtGpqrHx7OtMPE6vOG31stlhSAoWFVW5JsM7np3vEc9H1HI66TrZ+SI1F5N+YCNu3AoWYSNtDgLnAdSJyVWUP0pFMcIa01i7+L8AEQl0WCOlTGEjyuwOpZ2JfM4sVPTvw7qPncPecJ1iyd7hlWiea58wPyd9vQ+qTTx7nsQ8A3e9+Fq68EnbYgWOb7weYda/D2ZEjMUYLntAu8wukalg/8sIDHXw/NMhhBg2Ho7aT7QxpNnATJqX5jUA3Vb1MVb/CWN5NAa4WkQeycaCtkwwbllQ0nYMybu7dbBdYv5xxdh3HcyItJNFkOzgj8mYRAO3sTGe9DV663hfENP+0M1jVtR0bC8PXk5pZUZELggLJux5A05feTqhbb92GJMGYlGbjrrviKTWqkBcPNdvG7VLXczjqOtkKpPqY3EHdVfVKVY2ZOqnqfGAPYCwmkverIpJdFrm6xMpEB89n+IRXfWmfls+EX9+Nbu5J++/5nYWsiplxF9lt0KihLx0i+/ICsN7OSBTlCb6MnfOEVdQsqCH102eeLSf+cEaecPEEcZtJiYYUTecvT2rv1f2ZBYlx7KoYLxhHu21T13M46jrZCqRuqnq1qq4IO2kT8R0AvA0cAXwkIs3C6tZ5vv464XAeu1BsIymsL4J7e8NLf07VQXwCOpE/YvvzWcly1iaJiEycbMHMjpb5fJR60oZmNDQqPi9Vgy/c0UZK0vpClRdvzKcyOG3dpguWJxlmeO0Xsgo22DHefXflDjID+hwCTTpCm+RlOIfD4SNbP6S0MWJUdSNwJPAIsBcEHEQchv32Szgs9RkGfHV7+uYFKdJFLGNtRmbfpzOE0xnCcKIdRVvRmPPZ16S42Mes38QcTCGWiXY5lR/G+nfMrKcZ6ePrDB6zgL+RmB7De8+taQybrMVg/dSm7Llg4QQXkcHhyIRcpZ8oU9V/ANeD9Z50JOLPWkqiQBp7c/rmies2ySqzYEmYQOpIczrSnJaBxHuRAqCLNYSYORN++CHhVDAJYGXwo535ZTK763P5/6g/KzmWXRdamgjpixebgjW5z9/koQqrF8CC783W4XCkJqfpJ1T1auCsXF6j1vLssxXuojutAfiG2QnlQnSMuzD8YXYWsYquhEQBBXjwwfi+jQd3LLsAiUFff+D30Kjb2eIJ3UZkuBT5YnJGk2WsMTOtUhszsE/VpM3QMri9DdzZySsIrzeLpUkWkQ5HXSVjgSQiheW5gKo+XNE+6gKn+ULE5Wd4/w1mg41Tfv3Qs3wTGisOgEWLkoq8/Exv8mOsbASTo/vIghYU0p5mSbO7LdYb4beyS5vEBiF6Mc9isKTE+jRVkdn3osmwPtnOIoFiSnmWb7ifL2IPEA/wBQ/yBRP5g5v4gDf5MefpPfysY1OVpKV3OMLIZoY0S0TOE5GsvSBFZAcReRu4KNu2dYUCn+lHpr4qG3zm2X4KqZ+QfK+8DKNfYkGnTkl16qf4CZXX+q6UMpazlgbUC82Ie8yyngD8eOr+zB7nSyJYlJxwaDs6A7CpxPZTRWGDZn2WeDwsxJbC74w8jcVspISlrGEJa3ibiZRQxmTmVcpsM1PeYAL38HnOLCcdjlRkI5BGYgKlLhCRB0VkaKoZj4j0FJEzRWQc8AOwA/B5xYa7GXHggQmHjdvH9/1P1hEZzlMSvJl0In2onH1JNgFLSlMesAyERH+nYhJTaSwppyrqfX7iPkaxig0J6kSPhjZG6opu7WiW50vx7oUG8uGpH+vf84ApmJmbuHtBFk+O7/c9HAael1zHc2IGeJnx/EZ4pK2fWcD/+Iz5VZB3ygvGez3v5/RaDkcYGQskVT0R2A0YD5wBfAKsFJGJIvKhiLwoIm+KyGgRWQRMB+4HugOXA1upavbJbDJERA4XkUkislFEZtmo45m020ZERorIOhFZaoVt7v3pn3wSLr8c/vIXOPRQClvCFcmZFtAUyVKjZFWp78zu9IxFvU7FToRmEkmkg8+XaZttgMRo4+8yKaH6m+V8sp/AXMBkrQ0zxpASI/g0P4+8PN+Mp3375LrejucQu+WW5RpTtvz4ZHz/l7fC6wSTDb7KD+EVMT5ZXzKjMoYWSdB8/zreczMlR5WSrdn3eFU9AOiLieo9EeiH8T06GjgMYjm23wCOA7qq6i3WHDwniMhge71vgUOBJ4BbbU6mVO2aA59hQiAdjVEp/gXIfcSxDh1MLLbXXoN33gEgP8wiOcX9IEpd5l8D2J+tk6I2hJGx4YBHw4ZQUkLB3feTt8moDn9ifkyYACxidYXXI0JXw/72NwB6jpxAWTdf6OzLL0+qmofQato86o/4wBQMGgRAyUYoi87yXqnsFjI7ApjEvJTtjmZAwvHUHFgyApRRxgJW8j8+SzqXC3N+hyOKcq3wqup04D9gAq0CnYHWwHpgsapWtZHrVcBYVT3NHo+0GW2vEpEHVDVk7gEYC8BC4FDP2VdElgNvi8gAVR2f85EHaN4VVvqsl1Op7AqozyaSM84uyKVqZ8wY2GMPYxzw1FPk/esC9p17OB/fYT764CzpXSZxQsA/KBtCDTe++spsRZC2vng8S5Nj+grCti9+ETv+eWRT+v0FbmwIefXgyvBluAqxKaCp7LBjdu2v4pDYfndaM5tlKWpXnBv4IOG4E81j6sFVbKA1uVEYlFJGfm4NfR21jAr/GlR1napOV9WvVXViNQgjgB0xKkQ/I4GWwO5p2o0PRJ4YiZmXHBLeJLdIcM09hUAKW/AH+DZgBp4pbTO58QwZAvvua3I6WWnZYvbiyOqzKngzTRUFYvRVx9CUAnjzzcg6Aizetlvs+NUjTSQMyN0M6UGf593hT8O2xybX8dbbetGWC9gvuYLlRAYm+JxtooSZLOEOPq5QhIzZLIulKglyWkzJkRjXMBsWspLreI9SonXON/IBdyb9bR11mc3l8aQhJOW69lSEWxNNWLsSoCxNu5yRlw/1fKYiqWZIbQIOrRXFs0hLS34+lJVBCxOqJ09S/4xKKeMpxjGDaMHlkc2axcqu7cwT9uGHxwtLEqVMGUpeSeKNd37IvHftYpg2Irm8PKyYbbYFzWCHE6FeiF2qN4ttTWOaUBCLlrGPzQrs52L2ZwtM2vuNlPA837KWTdzNp2nHMoJJXMd7CYJlOWt5hq+5iQ8jP++/swcAr6VY10rFI5jl4hv5INQa1DOe8KcYcTg2F4E0A6yHZhxvJT/CyzPWbgcR8a/e7AzkR7UTkTNEZLyIjF+ypPLzD0oelPjjgKa4PwefkI9MEQIoE5qToZtYfr5xNC02qh9H7AAAIABJREFUNxotTT3V+JKZ/M5yPuLn0PO38hEv8R2Qfl0FgEMPhTZtuLzg8GSjh0AkhhY0os2viX0+d0B8/1r7D3hqbxOVe00lLtPsc2Ny2XqKmceK2MzBC3q7FR04kYEMomdSm3rkx4xOgqnb0/GDXdO717c+dB+jYvtR6sBMwjVFERRyd/IJ1/FeQjSPj5hS7v4dmy+bi0B6CDhMRE4XkZYiMgzwUpyG6yUMjwJtgXtFpIOIbAM8YNuEtlPVR1R1gKoOaNu2bSW+BUNZ4KqprOyC60e9SBzP/5Hd4oX/SbYvyRZrMTyBtMqYLTcvTr0UOQqTOnxZxAL5RkqYZmdPP/qMIg6kH1dycHKDevUSLf78XHstqjDzYyheb0MmpZpmKiz9BZbaHH9zx6V8K1mxvvk65rCMTcQF9u2M5HG+jD1MeGsoeQjdaU1emr9kKku8VGxhn6+C64vPYjyyh9ALgIMw1pN+Q5gof7covmB6wrGXEuUVvmcEk/mC6QkuAeP4LcllwFE3qfpsZbnhCYyf04OYoK7rgH8D9wLJ4QUsqvqLiJwB3IVJmVFm22uqdrmkKOAms3E11G8UXjdI0CKtWaYznlh981S8Je04KmDhlUB+PkyZEgtU2qZV16QqJ7E7T5H93b09zZjDcs5mb1pFqSTHjIF2EcmF7r6b/715FyvnQNchMOyDBrSYZb7K/xHugzTjw/j+mgqugGoZ0KQEWf0RXwCeOcXpDEmYgb7NRCBz68ao7/IHfmdHukQKshYUsoL1NLR/9UcJ97zoT1f2CfiibUl7prGINWyM5aPKhNEBgRQcb5CPmcrHTKURDbiI/TO+jmPzY7OYIalqqaqejZntbA+0BzwvzmRvzsS2T9j62wOdgLOB3unaVRWlKVTsf2W32NrC8eyapL7KNoCQFwaofYgzagIrV8ajZwP1n32Bva5+PqFKF1rGboKp8IfFWcLq2IyhJSmkcJs2SfmkEoY3x2x/Hws/jyil5W8LKSmoz4oQdRjAR/+K70+qgMH/2iVwXT4wOlkQP8rYUPVY6wzXAXuSGCbJy/g7gsncwAcsZFXSDLSUMlbYnFJFrGcWcSvEw9khti8ILUI+7y42ncfICFVrOoLR19Oxjk1Mq57nQEcNYbMQSB6qWqSqk1V1Dcak+ytV/SWDdhtsu0XAXzGfyys5Hm5GBFV4fnrShpMZxFUcQi/aViCCnaEzLTiWXRhs1TeReFG/TzstVrTXdYmBTQWS8hOF4V80f5DRjOM3CqgX6hAbo3592DXg7HvEEaFVv7y0Phubhwu382Ynl/0xDr69P7WqdAJzmR5ioBGL0r4yXBCX10DAYztM6KYetGGrgEr1EcZwv29taBZLudFnzv0HRTH1HCSqd/ciPOCsNyuaERFBIgzvAaMljehG6+TwU2l4ifHOGbcOUykCSUQai8hOIrJHZfRXjusPFJGLRGQ/ETlCRF7F5GQ6M1Bvhog87jtuJiK3isghIjJMRG4BHgPOVdU0oTGrBq2Aar1BlhpZQehDu/TttkufUUSQ0AgR45mTcByWtmIjaeyxw9aEXo1n223pV83NboSsVxZ1Tb7ptuiWVATAB2fDPSEyuQzlDSbwLpN4ke+SZjxf32V35scNAnale9S7yJqD2Jaj2ZkT2I3OEcL+EcYAJAifIIXUpzEFsT6iQjz1J66KXcemhLWwKLzoHE3sbLtjirBVQyIefEpSmIo7Nm8qJJBEpIuIvA4UYUIKfe47N0REfhaRvSs2xIwoxkRaeAt4CmgEDFbVSYF69SAhkVApsBPwrG27LzBcVZ/K8XgzJtWTepDgrKI9ybHdKoWCEDvmvDwu4QB62JQYYeMBE6euQrmT/vgDfvop2fcoLw8eeQSAxr7ZyxaMpc+n45GIm1xexNLIitmwPBCpZyZLEqKYP8PXFNlIFNPe81U8MD6j+C6FT1gXq27NlIbUZytrldeUhoGcWIaFvvh4UexBbyDud+ZPFe/Hn4fqv3zMLXyUcH4Za/mInymjjEn8wcdMZQoLYufAWAhG0c33WzmPfWL7Y3IcIslRcym3UYOIdAS+way/vAO0I9EJ9RtbdjT4dAk5QFW/J9nsO6xe98DxWkzYoxpLKpVdEL8A6ELL1GqvirAuJBxQWRkNpQEnvPQSHH10yubrk1y/suDqq5MvXWr8t+htbrSNWcTJY+HJIXCK9afpNP0XzpsNv74NH54HJ9u1/bIUBmTzv4dWvePHL1rTdD+fMJXh7MwcLy/y9quQVvFOj2VXXuDb2PEgetGD1nzDrFguqfJyCQckqOUgvg5Yn3yKKaUtTehBmwRnaW/96U9sx0o2cEwKA5b+dA01RABiKsJlrElS6x3BToCJ+nACu9GVVnzGr/SjI21pwhyW04u2CVEpPMYyI9Qfy7H5UxEru6sxAmc/VR0lIlfjE0iqWiwiY4DBFRxjneL/noM3/xo/XrsY2mbooisR+5VO9+7R5445Jq1AKsjCYiuJ+Yl5llbNg7u6wJEvw1btjBlFfdbRdTCc99ksfA/etOgGu51rXpmwzt5jZ7IkKSSSx1QW8vap8OMT5lgmjomd8262B9KPfPLoT9fYQ0LQRL885JPHALoy3icw1rKRmSyJmVGfyV6AMXDYkvb0IW6dmEceJ7BbymsczDYJAknRpAedoDA6gd3o4TPC8Pb39/ma+8fh8Q/25CFGR17HsflTEZXdwcA7qjoqRZ3fgeQkOo5IgjnmNqwIr5e2n1z+mf1rOD16QONoS7FjGMAe9E64Ga213vlzfGswGauvyqzq7V/GNM7zH/rxKShtalRAWww042t8z2Vpu7vMN9k7wUax2cI+Qn1wDoy7y6x7+Z2QBwbScnjCKIpd6cHOdMvJd7IzZiFsO9/f7HnfjMzjELYLFQLpyCOPyziQNla95xkcbEzhm9Tdp4rLhnY+FfNSl0W3TlIRgdQeUjgcGIqhkuPbbOZ8e2/52/pveDkNybLaF/D0mWdgbXRE6C1pz1C2SliP+BgjRfyL6X7Lqis4KPraI0ea7fDhpp1ttmgibFht1ita9y6FqVOp/9ZLsWYreoQ70tYvhI79YY/Loee+cLXCCR/7LneB8mvAFLkTLRJVTS94aTbi7+HCFPHpKpP2NOMyDuT/2CnJXL+gktwM65EfMwGfzXI2UcKtjAyt24UWFRK8nlXeg4zmv3ycprZjc6Miv9jlkDaJzpaQo5j5mylLf62cfnJm0AAml5NHtwhTtQB+Cy3PispvTVdmy9rSJG20AsBEigBW2cAOq+fDk0PzOR9o/sOb0O9vCdUf+Ok+OvIVJzMoqaszvk88ru/3Qd0qWdjO/6WEfn1AFxUgnTYix85HxzeHkXE1lbeWUxV4hgOnMoiHGM1ya2jhD5JaUTxDlOf4huMC1pOXcxAllFZMFWvxR/9exybmsCzB+MGxeVORGdKXwJ9FJPTRU0T6AAfissRmRcse6etkQk5Vdv6sqxmmBA8TMp5pcFuaxEzNI7PMlpXB00/Hj1ubm9QfPutmtddo83NiRrz1LRpT0qghc31x4BRlDNPTq4bykk3Mxz1ezM+vQb1D4+svcsdUaGnUWE0rEAeuItQjPyHzb6ZOt5lwNkNj+/7U63vQm3zyKkUYQbLv2tN8nd4NwLHZUBGBdDsmWvYXInIQxtTa80k6CHgXE4rnjgqPsg6xy9lm2zC9T2lKciqQPvMlcsvL7Cc0ORA09Yvr4mq6w9iRORi3L88CLInPP4eTToofb23WpH54JF6kESbGhSsSZzmbKGENG/mcaTwQC+4TwRYhKR46bWTE36FVcVP0yfh4ZbQJ7hHlaFoVtLRCaNtKXrptRAN60Jr65MdiE17E/gytZGu4TiF+S3c41V2dodwCSVW/waQy7w6MwGRbBVhlj3sAp6qqC+ubBY2s1qd+BR9ucxqCw+8YGzZDmjUrqWhvElOHj1o6i3es5VpD6sX8lyKjRKxItO7QMrg2IHPXpwzsbuK6rWYDt/ARr6dJr97Gs8GwEyQdsjt6T3dzUAYbV8Km1cBzySk7egTC/FQlHWjGJRyQdWDd/2/vvOOlKK8//JxLb9JFQIqFpoioKCoIYsMa7N3EHjWaRKOxxBZL1JiYYkvQoCb+LIm9i10UG6iIBVEUpEnRS7/ALef3xztz7+zsbC+37Hn47Gd233ln5uzcZc++73vO96RDJdUxIqj5WqNKRRU1tXlNqZJzN1LFDBag3r+/8goP8kHGKun1haIsZEXJqlXk9IlS1XtE5C2cTM+uuKqxK3E6cLepap5WREoHv7SQL/I57U4YPCH94/vRhXn8yMocirdlRMeOLjQwGHn33HPwi1/EdAuLc8rfP4/ZdxDb8THzo6eZli+Hyy+PafpzxACgKsFUmfbpQxtasIKKWoX076gT4phPOX3ozPesYjrzOIBt2WnyEn6YBS1aljlRw41lcMVAtEzhCjcqqK4E3osfyrbJ0/RVtmQihJoJa0P5Y4Wq9vozdqMdLVnCqtofDuvYQEda1ybnXsr+kYnBd/EWP7CWmSxkV7ZkFetZxXq+YmlkzlNDYyJTWMJqtqM3e7A11dSk1pYsMpVU8w7fMITN6J7ntep8VIz9SlXPV9XdVHWgqu6squeZM8qOVt7ft7n33TrnxcR9o/AXtINfuOkw6wlYGJ/3mZqWLWHnUIJnmoEOPmUIXWjHXgxGFFeiPCDeysiRMKtOkvANrmBtIPBtz2tclFxk9tVVVyFTptQWqJsXIXB6D1OpoJKJTGE63zGfciZv/iHT9/mQd8d41fzaV8GqFnDeUKhwX4QVP8CAsc0ZcPz4mPMVyiHUN6cFUgqDygr5ph9d6EZ7tqFnbdvnfM8HAdmp2xLk2q/znOY3LGc5q2P2Pc+nDX7kscSzeSYLuYM3+CdTUhxRfBZQzuvMjtRzzJUmJa7aFOg7Gg64DcbGCxKkRaKy5ql4+DC4dwzcNw6+fCrDg199NbY+UZK8pCiCIeFMnQqjRrky6d95CZmhZNjX+X3M6z0uhb2ug2OfgornQiLtV18d4yA/CGnp+dwcCGO+L0rofVXdZEK/MW5btR46bwXHPdC8trRE0pD1Rk6wVEYuBfzSRZBaJ7iIFbXpApD4cx7UYZwc6A/ub98Y1cTfJ34KvD7xBXQzlb5KB3NIDQwpg11+Abucl9t50q7+Sp1eXtV6mPs6PHlKhhdr1w4WL4YXvMJCV1+d0eHNgx/D0V6o8ltv1Sk+tAiPOJwDa9PV5Q2Ved9Bgw6BNgeMdBVlQ+zjRZ8tSUPrLZLpdVNzGwKn6OAtIf2KvbiSg9ILWW/E/Jw9OJqdiqai4AvARk0PzmEZM1nIR3xXO/JJpMvn8zDTk+5viLyQZfmPQuHf67ICfAZy0bL7Js2uqqop6hkYYfxcmOGnZnf8/hnI/leHpOUq0pntmz07rlw4bTyj33wzrnt32tOhsg2rW8R/YdR+iYcCF3jXG6kEEnH/Ehjh9E0kSvXUU24N6+CDa5vah/KCDmE7XuHL2imeTAgWTPzuTVwpyBKhB5vUy5pGVC2poCJFS5qzLb0oQ2JqbDUmMq3MW0gWsZKebBL5w8O/u4X4UZLLz7ky3E/V8KMTLvKuP9Ayx2uUNO0380RDM+AQhgHQN4Nkwpps0jwGDIAddoht28OrPnLFFbHt8+bR7pGnWdVyL/SNJJFwd90V3xbSxVtF39qQ+KTCs7ffDgfUTZ/1CUXgbU+fOAmgZGy+Gww+DLoOgm0DJjUrXv6rAfyEYTEyVD5+8EMn2tKLTjERgGczpvb5poVMGM8RXzne5wL2rn0e5ZALwQ+s5Rqe5W7e4lqeiywt7zv8QoyRsx4hhZWzg4jI1sDfcbJB4xP1M5IjZZmVnwDYgT7skFJAI5bK5LMc6SMSL8YHcMIJ8PbblLGRHV58jIP3/BOVbVpx2+x/srpXl7qfLF9HlB34b3ydxI59ncZfJs46XIFWcCHmQ+gZU9guEadNdQ6wptI5oRd+5dr3/2v6Nhi5sw09aUnzmPUkn4f4gB9ZyzB6czqj+JSFdKE93WjPGAbwHt8WZJopX7yCC9wZwwAEiVH7+Le3rvlz9sjbCLWamlq1+Da04CL2YwYLYvrcwAtx0Yl+n4Y2QkqIqn4NHA70xqmCG1kgzTJ3SNnwxu9T90mbsrI6AVSft98GoC3LOPiGPwHQomID5/c5mVE3PeL6rF9fW88oGUc9Aks84e2Mgy8CiPevK+3olyJ/yS8TX9bMRT+KwLjrYMcznHM0Cstg6gJm/KCFIcQLxMz2or78XKWh9KYXHRGEPRlIbzqlVS+q2CxlNa8zm2+8EvM704+xnlMK53rlK+qukuqY0iUVVPISX/BWGrWofBmpQuR2FWw6TVXXAy8BxxXqGk2dbEZI2bBp6gKw6RPlkDyGNnskrm3c7+53T6JqLEWwzRF1z3e9IGPrIkmklXYmo+lFx8jKt2N+B4ek9p9GHjiU7dmSbpwSKLd2JDsm7O8rk4fxNRSrG1hF2nuYypueTnULmsWMjH5OfBHuZErr6RIlvvwO0WEBwWm7YNj8ZkmqAWdLodd3qiDip4yRFjVV8P3Hhb9O83yug4hAVfSiVNvqeJ3djS09VYMNqdXJl43/NQDbe7qp+/0pM9P88gvhiYagXFEwtHkzOnI6ozMuBW/kl5Y050RGxqwDCsJ5jGM/hsQlUyfS1Vvm5fjMYAErSO8HUKGopJpH+ZDVrI/R6guv2XSibVyEYSKl9UxIlad4BQfWPn+YabXP5wRqX/VpTGHfItINOAyYX6hrNHWqKqBDEapJZVKVNiUbN8LNN0fuqo5QwG69YSlccgm8H1/DJ+74G/8CwIR74PKN0ctVyfDXD/Zn25j2YASeH3XXPcGvbKPh0Jm27MqWnMNYfsqute0tE2ga+sKzzzCTv/NavdZcephpfMZi/sIrKfu2C/xI8sk1wfdJZgBO/mkQPeL2C1IrgfUNy/kXbtr949AaU77JJez7yiTn7ANMADoCl2Z7jVKnywDQfDqLBBRjWhBcJddIbroJBqUW6eyxvduKQLMsxBAOYjta0ZzhoaCPoATNMYzgYabltXSDUVgEiSkKmCjse1t68Qwza1/fwRscw04MYjOu4VmAoskL+etFYcJq5+Aq6f4xNCpay8a4VIZ0mMX3bBYIijiPcZSzLqbmlx+scCK7cC3PAbCQFbzObD7HaZr9ukBKHbnMRVydYv8q4DpV/WMO1yhpyprlefQSYvmXcPsQ2OXcApy8piZOCXwoDybu/2Wd0tT9PM8Jl0/lo+sWsSP/qm3PdEQUpj2tODSB6OhhDGcRKxlEj0aheWbEcxZj+JLvGZkgnD9KDPZhpsf8vZexOu/6bOmS6HPXmhZczoEI1DqIVVRk5JAU5T+8FxM+PpL+tKVlzDT1+exd+wNNELrRjuWesO2bgXqsm2SQeJ8JuTikcQnaa4ByYJaqWiGTHMh3lF1lhVsv8gVcP30I0Pgqtd23jTs0fQYOdEmzqi5x9vm6SJ6Oac7ezmF/rrluf4SqWoe0gJGJClPkhe3ozXbEK3cbjYdN6ZAyz+hMRjORt2La/NERuEq1hf5BEjVVeCIjI3rW4U83H8fOPMgH/MDayNFUIuawLCKXqe4X3i/Yk7VsiKvl5TujYpFLHlKKQjJGrkhZ/qbsqtbDH9rCiHPgoNtd29s3RvfNyQn6uUTz5sHdd8MNN2R0+JNMqrMj8PH8tNu5BXVIRmmwGR05n71pT6va0UaYGmoKKgF1P66q5Hi24UVPFmjLNEuWdPHy6WbxfUY/oL6NSKwdSf/a511pF6m034MOtYKvPoWUjWoyKgoicqiIfCIiG0TkWxFJKyhYREaIyGQR+UFEfhSRl0Uk+c+VIiFl+YuyW+bJYU27o66tKoEO68po/dH0GOjVPdqwAaYn0Q3bNnoYNjOUJXAjK5jCZXyw/JjI/oaRKR1ojSAJp7yykZPKhFWeMGxvOrEFXTmQoWkf28VzGl/wfdqBDU/zSVxI99mMoVMoWTyKM9mDi9mP37JfoK1w66tpj5BEZFLqXpGoqp6W5bFpISKjgMeASbhCgSOBm0SkRlUT5tKLSB/gZeBD4Kde80XAZBEZpqq5fDXnzPoVTj4oH/jOp8ewurZug2H5rPi+lblExF5+OZx4IsyYAZOThKf+5z+wY3wuSXVoymADHXmV6xlxdg42GUYEZzA6MsptDssTVy7OA73oxCJWsDmdOSkQHZgOwdHJKtanJaL8UWCq/GR2Y3M6p61Y4ZJzXQRRMdZWM5myOznLayhQUIcEXAm8paqne68ni0hn4EoRuUNVE/3kOQjoAByuqisARGQqsBw4ELizwHYnpdtgWDQtdb90WOMF0fwYSMSOckY54xfqOy5JPvT558MOO7DooCvo9ey1KU/ZaQvYO7OZP8NISXiE5EdYLmZlwRxSDcoiVqTumITN6cwCynmVWRzGDqkPCNA3hSpJfZOJQ0pfibL4DAduD7VNBs4HdgMSrXe1wCXvBlcZ13ht9S56lc81pKe8nwSV62DdD9C2a7QSRKf+sHpR3OHp0yFFhNKkSXCKq2/Rqk30mzvjA7jLq/m39w0w+pIc7DGMBAgS86vfL5P+PnPjctXyxXUJ1q0yYRA9WEA5M1mU0CFtoIqlrOYepuZ8vWKStkOq7+mrFLSGuIlfP/V/CIkd0qPANcCfReR6r+1KXJTg//JtZKbkM+w7WMOnwnNIUcELNdWuHEX1RmgWn4+Xml4pMnm33rr26cZN+8ftHn4ydAwUnB312yxsMIwsaJthpd9qaijzNBHT4YFAuYxjGZHRtYKMoF+tEGsl1ZGl3J/g45jcIoCj2SnraxaLphLU8DUQqqNdK0CWcIyqqotw4etHAEu8x+HAeFVdlui4YpHPsO/dL6x7Xhbx/67vaBh2Igw+1L1OFPCQkuoUHjSQTNR88JZxuyfcA+26B7o3lU+o0eBpE8jHWZNG5eW/8Aqv8WXKfuDygL4OyO4MjFBHSJdgPtW9CUZAYWf0K/aKEaltqDSV/+7/ACaIyBki0llExgO/8fYl/IYUkZ7AI8B04ADvMR14VkQidZxF5EwRmSYi05YtK6zPmvU4rMqT8NL6wLR1VNmG+e/AYf+Bzp6P8B1h9UbYuNZt0xqtJdCxq6WirtZFiw2xelqLEyStGkaxeYj4xdulrK6NwFvmPX+LOVzDs1RSHRn1VkU11/BsrVRPvujmRdstZlXcdaN06opRcj4f5Kwa6X2p740rNREVR6mqmnrlOjcmAdvjghAmAutwdTxvhdBPhVguwt2DI1W1EkBEXgW+wkXr/TJ8gKpO9K7BiBEjClua0htMaE3uI4XgutDGiFw3f63Kv47vkK7z/qKbDnXF6Y6OF+yOJYHS9+18xskH3kS7cXX51NLW/SeZyoW8xM30Hgl+VMr58634nVF8zmYMd/Im7eOiPav4B2/SnlbszWCWhZJbb+AFALalJ0cElMin8x0An7Awr3Yexy7cymuAU28IroUFBVC3oSfb0LNoJedzJSeHJCK/By4JnUcIVrl1zwvqkFS1GjhXRK4ANge+BU9JEa+yVTSDgc98Z+Sda6OIfAbUe9n1HU+HqTfD2qW5h39/81LgRYQb7TLAbX2HVFNdFzAHsPRT90iFduoc+dFfzjasufE+2gU+Ka2PHs9Lv/gjH+HqtA+aULdvE8uCNeoBv3SFolRSzVx+4A1ms4iVgCvb8CQz4hS4fT5jMYEKKbWJrz5b0o3D8jAT0Jm27McQJnuFCqupqbXJL69xHuPiClM2dLL+3S0iJwBXAFOAI3HO5z7geOAunITQQ1AgFb4IVLVcVWeq6hrgHGCqqiYLbp4HDBWR2sljEWkFDAXmFtTYNOjq6Y1W51j+RDV2TagmNBoC6OuVXRFvOk9r4NFjM79Wedu64kpPEVuSPFzmolW3lny6+UVUeMKYw07M/HqGkU8EoQcd+Jpl3MALPMgHtc4oSLKaSi/xBSup4K8ROU4nMjKm3lEubO2VUwGYHyiWV+HVS+rYSKbpguQyEXQ2sADYX1Uf99rmqupDqnoWcDBwNOSp3m4SRGRXEblQRPYRkcNF5H84J3l2qN/XIvKvQNPdQC/gcRE5SEQOBp4AeuJNy9Un/lpPrqHfNaFlnVmP1z3vNyZ2G5yy+yy+enhKqgJljSq9ee5qbwDtj8KCnD8fWntlVbJR8DaMfNOaFmmrIOxFvEr9O3zD33i1VpHBZywD82KfT7AQ4Yt8BkA562oTYQspf1QocrF4O+C5kIBq7XK5qr4IvIhbpyk0lcAxOGdyL9AWGKWqn4T6NQ/ZOB3YH5cc+x/g396x+6pqflchs8AfreQa+l0RkrF6/SpYMdc5nepK+OU3MNwrehdeQwrzyDGwLlo53x0XsHU9nVi01dE8ykPu3Ammsbfcx22bF0ZA2DAyYl6K4nVBRrN1TDG7KEbSn5+xG2OJ+EWWI36ZlCWspgatXVdqrOSyhtQCYhT7KiCupu2nwFk5XCMtPMcSDvuO6tc/ou0VSKNKVj3gj5DCI5xMef+2+LZXLnPbBe9A50DKs++INsTPUgBu1LR6MZzyZvT+miqYybFsx0MsYRgfjHmYL+Ykt++gO1z+Uev8V0Q2jIwZwKZ8xVIATmIk7zOXAWzK96xkkfcIIghHsxPlrOMlb00nyF4MjswVyge9vK/cTenA2oiy5I2NXBzSYtzUls93wLBQn96AlaDIkkovQnrNYuiWun5dQlZ8G9/2aYLSRL4TnHJ99H6A76ZEtz/9c/hhFszjQT7e+wFWvyJ8fI/bt+MZic/XthsMSP4j0zCKxiEM4xZeBmALutVWTvWppJr1VMbkA/k5PktYRQua1UbXHcx2BXNGPl1pxwrWxejyXcz4gl6zUOQyZfcRbtrO51VgDxE5SUTaichBuITTj3IxsJTp1N9tcw357u1pl2++m9tuliTIp41XeHPmA5lf58PP9zINAAAZeElEQVSJMM8bOY38dez83GaZSW4ZRr3RnlacwC5cyL6R+1vQjA60pmXE7/lDGc42gd/p2VR1zZROtGVjIN3yVHaPLEbYGMjlq+4ZYFsR8Sd8bgRW4tZwVgFP4SLvLs/FwFKmLBDxlgt+sqsvUDo0oHt69sz4/tkwNyTO1GXr2NeJRlWG0RDZiu4xlVQzoT9d2Y7ejKAfAwKRcIViBXXy/K1pweZ0Lvg1C0XWDklV71XVtqr6rfd6Pm4d506csOlEYGdVTZYHZCQhmBOUC75D86PYfphdt69tqC7YkjRDOTQUhHTfnrGvw+ed37g0Hg0jawThMIZzIEOLkpC6L0Nqn5/K7gW/XiHJyCGJyE9EEk8gqeq3qnquqh6gqmerap5+f5cmkmXY95zJcN84eP6XUFFe55D8KLagAkL4rznnxehzbhuqj1dVEd3Px5/688mXarlhGLEER2H5ynGqLzIdIT0BzBORa0SkX8reRk5kO2V3/3iY+zq8fyv89/C6EZZ/vmDVWAmtt+4QqlzVdRDsfSMcel9sezDyrzwiaEIEfhuIwdzmqIzegmEYaSIIJ7MbYxlImwwVyxsamTqkV3CJpJcDc0TkeRE5TCT8tWbkBW+0v/K77E8x93V47ATvdBF/7bDQatghtdsURl/sVBaCo56gQ/o8gb5dm4DO+pDD0zbZMIwM6UuXguQ5FZuMHJKq7gtsCfwBF/Y9HqeWPV9ErheR+HoCRtb4eTnNM1AAWb04vq3aS0+I0sML/5QIJ692D9QpG3dN3fPKwJTdy0lqFvmOqJXlGBmGkYKMgxpUdZ6qXg70Aybgou26AZcCs0VksogcKSKNM+6wAeE7okym7CrXJd7XIkJnsVVEgdeuAYWToJzPiLOgj7dmGlZ/SMRP/gWH/x/02C51X8MwSptcouxqVPVpVZ0A9MVN480D9gEeBhaKyE0i0vjHkfVENlF2yfTgWrSFwYelPsdJAWXwjatj7Rl1sWdTmunOrTvBdsen19cwjNImL+p7qvq9qv5BVbcC9sWV/94EV1MoXkvDSItUunIAz5wNz51X9zqV8wqGX3dOUGCjY6A0Ybchsfv8arOfPpz8OoZhGJlSCDnYN4BHgRm4ZfnGURmqASKhKLvls+CJk2OL7U3/B3xwG/xe3CNV6fH1dSr1tO2auJ9Ps1BuoD/tN/WPqY81DMPIhLyt84jIIFzBz5/i1pQEVyjvX8mOMxITHCGtWgi3e6OVGfe5xNOLIiqoV29Mfs4t94WvnnXP+41NbUNlKN+oTZIk8JNehmWfQZ9Rqc9rGIYRJteKsa1xNY9OB0bhnFAl8Bhwl6pOztnCEsZ3SFXrYc33sfvWLY/O/1m7NPk5B02oc0hlafz1g0rgEB+VF2TLvd3DMAwjG7JySCIyHDgDVx12E5wjmoMreHePqqb4WjTSoYWnrFD+DfTfM37//Lfj22oSVJc98Ha33fF0qPgRXrkEtj06tQ1LP4t93X2b1McYhmFkQ6bSQT8XkWnAdFw11ja4AIZ9VHWAqt5kzih/tPQKQrbqEJ3U+vhJ8W0V5fFtUDeyEXGJrldpctVvn89DVWNFYOdz3fnmTYGNa1KfwzAMIx0yDWq4E9gR+ApXCXZzVT1WVV/Nu2UG4HTnlsxIvwTFlOui28OKDOkSVcW1VQenTXfvGHjvVte28y+yO79hGIZPplN2DwITVfWNlD2NvFC9wakcpBIz9Vk+K7o9WcJsMraIWBMKOsdXvcqz3QZnd37DMAyfjBySqp5QKEOMaLoNgYXvw4d353aecH2iVLTv6SrV7nZB/L41S+Lbci0iaBiGYV8jDZyaKhfivezz3M6TqUCrHz4ezkMC+CjCOa5amLlNhmEYQcwhNXC6DXZrSEEJn2xYl6b2nM/gQ93WD6xIRZSTMgzDyARzSA2cih/dGtKIs3M7T6blHw66E37zfV3oeZCdfh7f1mNYdnYZhmH4mENq4HTf1oVaf/NyZsd1HRT7Ot2Rjk+zFtC+R/S+g+6IbwsX8DMMw8iUJuOQRORQEflERDaIyLciErEcH3fM1SKiCR6XFsPuVEiZkw764tHMjjvqf7Gvk6mAZ2NTkCGHQ4de+Tu/YRilSdYOSUQilrsj+/XP9hrpIiKjcHJF7wOHAJOAm0Tk1ykOvRvYLfS4ydv3fGGszQzfIWVKl61gwEF1r9ukIaSaLUdn6CwNwzCiyGWE9ECqDiLSByhG0uyVwFuqerqqTlbVa4FbgSuTOU5VXaCq7wYfwHbALFX9uAh2p0TK0q+H5Ncq8o/b7891r9PRrcuEYIkKwzCMfJCLQzpcRP6WaKeIbIZzRr1zuEa6DAfCqyyTgc64UU9aiEgXXD2nB/NnWm6UNUt/hLT5rnXPm7WC5q3qXodLk+fKUY/k93yGYRi5OKTbgHNF5MLwDhHZFHgN2AJXjqLQtAbChRc2eNtQibmkHAm0AB7Kh1H5QMpSl5TwCVZxFSlssmrvnd12p7MKdw3DMEqLXCZyfgX0Am4UkQWq+hCAiHTFjVYGAqeoajFqi34N7Bxq28XbdsngPMcCH6rq7EQdRORM4EyAvn0LP29VtSF92aCqDbGvm7WK7pcvrtLCnt8wjNIi69/QqqrACcA7wL0isqeIdMRNlQ0FzlbVf+fHzJT8A5ggImeISGcRGQ/8xtuX1gqMiPQExpJiuk5VJ6rqCFUd0b1795yMTgd/2q33Lq4ExVkz4MQXo/v22yP2datNCmqaYRhGXslpqVtVN4jIBOBt4HHgG2AH4HxVnZgH+9JlErA9To18IrAOuBgX2BChvBbJ0bi6TsUY0aVNu03dduH7bttjmHtctg7+0Da2b6uOcNzT0LGfe236coZhNCZy/spS1R+B8TgnMBy4VFUTBjsUAlWtVtVzge7AMKAH8K63+92EB8ZyLC5Sb34BTMyaRE6lRRv42esw5sq6tpbtYeDB0GO75McahmE0RNIeIYnIpBRd5gEtgUGhvqqqp2VjXKaoajlQDiAi5wBTVTVBQYY6vFypXYFzCmlfVgSi40ZdErur/9jYCrHhmkfmkAzDaExkMmV3cpb9FCioQxKRXYHRwMe4kurH4UZto0P9vgbeiHCQxwJVQIMLZg46lSgH039cescahmE0dDJxSFsUzIrcqQSOAa4GaoApwChVnRnq1xyIqp16LPCKqi4rpJHZEMwfisolSlYJNt+5R4ZhGIUkbYekqvMKaUguqOp04sO+o/r1T9A+PN825YtUIyRwa0dDj098jiFH5NcmwzCMQpBnQRkj7wRGORXl0V0uTVIr6dzZ0KFnfk0yDMMoBHlzSCKyCdARWKmqq/J13lInOCpaGp6ATIOuA/Jni2EYRiHJadlbRJqJyCVesEA5MBcoF5GvvXYbgeVIcB2oIsOqr4ZhGI2JrB2Gp6L9Ak7dQIH5wGKgJ9AfuB7YX0T2U9U01diMMEFh1UyL7BmGYTQmchkhXQDsCTwLDFHV/qq6mxc4MAh4GtjD62dkiQSi6Bakm+JrGIbRCMnFIR0PfAocqqpfBXeo6hzgcOAznN6dkSXBMuJ7/K7+7DAMwyg0uTikrYHnVaOr9XjtzwNb5XCNkicY1DD2qvqzwzAMo9Dk4pA2AqlWNdrhklaNLAlO2TVrUX92GIZhFJpcHNInwJEiElmDQUS64QrezcjhGiWPyf8YhlEq5FoxtjvwvoicJiJbikgbEdlCRE4B3vP235YPQ0uVZNJAhmEYTYmsw75V9b8iMhy4BFeDKIwAf1TV/2Z7DSO2LLlhGEZTJtcCfZeJyFM4Ne8d8JQagI+ASar6Tu4mljbtTfbHMIwSIWclBVV9l/SL4BkZYlN2hmGUCqZl18ARc0iGYZQIpmXXwLEoO8MwSgXTsmvg+FN2rTvVrx2GYRiFxrTsGjhVG9x2/Yr6tcMwDKPQmJZdA8dX+O4xrH7tMAzDKDSmZdfA6bI1jL0ajnu6vi0xDMMoLLkEHZiWXREQgT1NVNUwjBLAtOwMwzCMBoFp2RmGYRgNgqwdkqdRdyPQD6dl9xWwBvgauBvYAri5WFp2InKoiHwiIhtE5FsRSTu6T0QOF5EPRKRCRH4QkRdEpF0h7TUMwzBiaRJadiIyCngMmARcCIwEbhKRGlX9a4pjT8eN4v4IXAR0BvYijyoWhmEYRmpEVevbhpwRkReBNqo6JtB2C3AysFmixFxvnetb4AJVvSvT644YMUKnTZuWndGGYRgliohMV9UR4fa8CtOISG8ROUREJiQKdigQw4GXQ22TcaOd3ZIcd7S3va8QRhmGYRjpk7FDEpFhIjJJRJ4WkSv9tRYRuRb4BngCN302X0TOz6+5CWmNC0MP4mkcMCTJcSOBL4HTRGSBiFSKyHsisnshjDQMwzASk9E6iYgMBt7C5RcJcCCwo4g8BPwOWAvMxI1MtgD+JCIzVPXVvFodz9fAzqG2XbxtlyTHbYaTOboc+C3wg7d9QUQGqOqS8AEiciZwJkDfvn1zNNswDMPwyXTh/hJcMuxtuCmxfYFzcWoMrwGHq+pKcFFvwKPe/kI7pH8Ad4rIGcAjOGf0G29fdZLjynDv5yhVfQFARKYC83B2XxE+QFUn4lXIFZFlIjIvS5u7AcuzPLYpYffBYffBYffB0dTvQ7+oxoyCGkTkW2CBqu4RaJsC7A6MVNVpof7PADuoau+sTE7frmbA34CzgGbAOuBi4FbgFFW9N8FxD+PWkdqo6vpA+8u4uk5HFNDmaVGLeqWG3QeH3QeH3QdHqd6HTNeQegLvh9r8159F9P8clxxbUFS1WlXP9a41DOhBXRXbZNVsv8CVzpBQuwCRGn2GYRhGYcjUIbXE5RkFWQWgqhUR/dfiRixFQVXLVXWmqq4BzgGmquqsJIc8g3M+4/wGEekI7IRJHhmGYRSVJpH8KSK7AqOBj4FNgOOA8V5bsN/XwBuqehqAqk4TkSeBf4nIJbg529/iBGFvL7DZEwt8/saC3QeH3QeH3QdHSd6HbPKQGmImbSVwDC7k/F6gLTBKVT8J9WtO/IjtRO+4W3ABEZXAXqpaXkiDveCIksfug8Pug8Pug6NU70OmQQ01ZOGQVLVo03aGYRhG4ySbKbtwAEAqGuKIyjAMw2hgZDRlp6plWTxsdOQhItuIyCsisk5EFonINV7IepNFRLYWkX+KyAwRqRaR1yP6iIhcJiLzPcX1N0VkeD2YWzBE5CgReUpEForIGhGZLiLHRfQ7Q0S+EpH1Xp+968PeQiEiR4rIVE9Vf72IfCkil4tIy0CfJv95COJJrq0RERWR9oH2kroPkGctOyMxItIZp7enwATgGlzy7u/r064isC1O0WO294jiElwS8k3AIbgyJi+LyGZFsbA4XIB7X+cDP8Elkj8gIuf5HUTkWFyS97+BA3CpFM+IyNDim1swuuLe++m49zgJp/JyS6BPKXwegtyMe49hSu0+gKraowgP4FKgHNgk0PZbXBLvJvVlVxHed1ng+SPA66H9rXGpBFcG2toBy4Dr6tv+PN6HbhFtDwDfBl5/iSvbUnvvcFJc99e3/QW+N9cDK3DLASXxeQi8tz2AH3FlcxRo77WX1H3wHzZCKh4HAC+q6qpA20NAG2Bs/ZhUeFQ1VYLx7rhQ/dpCjqq6Fngad8+aBKoaJQPzEbApgIhsCQwk9j7UAP+jCd2HBPyAy3GEEvk8QK3CzK242ZLw56Nk7kMQc0jFYzAQk6Srqt/hRkiD68WihsFgnN7gV6H2L2j692V3nJoJ1L3XcCL3F0CXIpdzKTgi0kxE2orIaOCXwJ3qhgGl9Hk4CzcSisp5LKX7UEuTSIxtJHTGTUuEKff2lSqdgTWqGhbBLQfaikhLTVBgsTHjBStMAE71mvzPQPgzUh7Yv6wIphWLtUAr7/m/cdWaoUQ+DyLSFbgWOFFVK0XigpdL4j6EsRFScYkKgZcE7aVEovuSaF+jRkT649aPntR44d/w+22q92F33PrJb3CO+bbAvlL4PFwPvKeqzyXpUwr3IQYbIRWPcqBTRHtHokdOpUI50EFEmoV+DXYC1qlqZT3ZVRBEpAvwPPAdTiXExx8JdSJWL9L/zDSpz4iqfug9fUtElgP3icifKYHPg4hsixsZjxER/+/b1tt2FJFqSuA+RGEjpOIxi9Dcr4j0wUXOJBOAberMwsk5bR1qj1tza+yISFucoG9L4CBvkdrHf6/h9YHBwI+q2pSm68L4zmkLSuPzMABoAbyDczzl1K0jLcAFOpTCfYjDHFLxeB4YLyIdAm3HABXAG/VjUoNgKk4x/ii/wfviPgR3z5oEItIcFzE3ADhAVZcG96vqN7g8reB9KPNeN5n7kIBR3vZbSuPz8BauwkDwcZO370BcXlIp3Ic4bMquePwDF030mIjcBGwJXA3cEgoFb1J4/4kO9F72BjYRkSO918+p6joRuRG4QkTKcb/+LsD9WLq16AYXjjtw9+FXuKi5XQP7PlLVDbjPw/0iMhd4G/gZzoEdX1xTC4eIvIBLEP8MF0U2CreO9LCqzvH6NOnPg5cC8HqwzVtXBJiirnxOk78PkdR3IlQpPYBtcOXcK4DFuCibZvVtV4Hfc3/cAmzUo7/XR3DZ+gu8ezMFV2m43u3P432Ym+o+eP3OAL4GNuCmsvaub9vzfB+uBT7FqQ6s8N7jeUCLQJ8m/3mIuC8nE0iMLdX7kJHat2EYhmEUCltDMgzDMBoE5pAMwzCMBoE5JMMwDKNBYA7JMAzDaBCYQzIMwzAaBOaQDMMwjAaBOSTDMAyjQWAOyTAMw2gQmEMyjBwQkf4ioiJyb33bkgki8m8RWSoi7erbljAispN3T0+rb1uM4mIOyTA8vC/BTB4n17fN2SAiI3ClL27UWMXxBoGqTgeeAK4Tkfb1bY9RPEw6yDA8ROTqiOZf42pW/Y34mkRP4ERCtwJWqurighqYJ0RkMrAL0FNVK+rbnihEZBfgPeB3qvqH+rbHKA7mkAwjCZ7ydj9gC1WdW7/W5I6IDMQpR9+tqmfWtz3JEJEvcIXrttT4Ut5GE8Sm7AwjB6LWkIJtIrKViDwiIj+IyGoRmSwiQ71+3UVkoogsFpH1IvKBiIxLcq2R3rm+F5GNIjJfRP4pIr0yMPlUnIr0w0mus4eIPCYiczy7lorI+yISOVIRkSNE5HkRWe7Z9ZWIXCYizRL031NEHhaRBSKywXv/L4rIoaGuDwF9gX0yeH9GI8YckmEUjv64aacewL3AZNyX6+siMgB4F9gZ5xz+C2wPPC8ifcMnEpFTcDWSDgBeA/4KTANOB6ZFHZOAfXB1iN6N2ikilwFvAjsBrwC3AE8DrYD9Q32biciDwCO4yqb/w9V9qgGuByZFnP+vnv174eoi3eK93gnYPdT9bW+7b5rvzWjs1Hf9C3vYoyE/qKtj1D/B/v7e/nsj2hS3BhLsf4XX/iOuaGNZYN9J3r6/hI4ZCGzE1UnqHdq3F87BPJ7Ge2kHVAEzE+zv4e2fArSM2N8t9Po2z94bgOaB9hY4Z6LANoH2P3htjwDtQudqD/QLtXX0+r9f358DexTnYSMkwygcc4EbQ233edtWwEWqWhPY9wDOIQwPHXM27kv+V6q6MLhDVV8FngIOEZEOKezpDTTDFYeMYrC3f7aqbgzvVFfpFHDTh8A5wJOqeqmqVgX6VQbe50iv/w7AxbhR3fEaiu5T1TWqOi/UthJYj5u2M0oAK2FuGIXjY41fjF/kbWer6urgDlWtFpElwOahY3bztmNFZOeI62yKcyQDgelJ7OnqbcsT7P8MWAmcKiLdgf8DJqtqVP/zcGtR6xJEJw71tuJt/fLbl0Q5uyT8iBu5GSWAOSTDKBwrww2qWiUikfs8qnCjoSC+I7koxfVS5ez4Id6to3aq6nIRGQ1cBRwIHAJUi8hLuKnHDwPd9/O2x6W45nfedjzOEb6Won+YNgG7jSaOOSTDaPj4zqujqq7K4TxLvW3XRB1U9VPgKBFpCYwBzgSOAnYWkd6qukFEWgPdgTdVdWyqiwb6fxyaokx1XBnQCfg23WOMxo2tIRlGw8ePiNsjx/MsBpYBg1J1VNWNqvqyqh4NvIVzYv7UmT8N1y3N6/r9N83AVnB2CvBxhscZjRRzSIbR8LkNqAT+4iW2xiAiLUUkpbNSVcWFdHcTka1D59hBRLaKOPfWuPWg74AF3nkqgE+AbUTk8KhrichoPw/J6/8p0EtEjo7oOzBBztKu3jbTaT6jkWJTdobRwFHVWSJyKi6v5zMReQGYjVtr6osbOS3DRcml4lHgCNyazteB9l8CPxOR93HBDUuBLYCfePtPDU23XQQ8CzwqIi/jHFQZLpJvJ6CFqgaj4y7BRQM+JCI/867RCRdR2EdVe0bYuh8upP3JNN6X0QQwh2QYjQBVvV9EZgC/AcbhvqzX4qL2HiGJ8kKIR4ElwE+B2wPtT+K+D3bBrRm19s79AHCTqn4VsmeyiOyOC+UeDeyJW+tajEt4/W+o/7MisifOMe3m2b8cmInTCYxBRDoChwLPqOr8NN+b0cgxLTvDKDFE5FJckuqOqvpRfdsThYicB/wdGKOqU+rbHqM4mEMyjBLDi3r7EvhEVQ+pb3vCiEgbYA4wVVWPrG97jOJhQQ2GUWKo6nqcTNG0hligDye9NBG4sJ7tMIqMjZAMwzCMBoGNkAzDMIwGgTkkwzAMo0FgDskwDMNoEJhDMgzDMBoE5pAMwzCMBoE5JMMwDKNB8P/R9hMG0TOQJwAAAABJRU5ErkJggg==\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Mid-price vs Time (sec) of the simulations."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_multi_lines(t, Spath[idx_fig, :], r'Time ($sec$)', r'Mid-price ($S_t$)',r'Asset Sample Paths')",
"execution_count": 13,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize Price Per Share vs Time (sec) of the simulation."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "lth.plot_price_per_share(t, pricePerShare[idx_fig, :], twap[idx_fig, :])",
"execution_count": 14,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "pricepershare = np.divide(Xpath, Nq - Qpath)\nidx = np.sum(lth.nan_to_num(pricepershare, 0), axis=1).astype(int)\n\nterminal_pps = np.full(pricepershare.shape[0], np.NaN)\nfor i in range(0, terminal_pps.shape[0], 1): \n if idx[i] > pricepershare.shape[1] - 1:\n terminal_pps[i] = np.NaN\n else:\n terminal_pps[i] = pricepershare[i, idx[i]]\n\nlth.plot_histogram(terminal_pps - twap[:, twap.shape[1] - 1], r'Cost Savings / Share', np.array([0.1, 0.25, 0.5, 0.75, 0.9]))",
"execution_count": 15,
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": "C:\\Users\\Sebastian\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in true_divide\n \"\"\"Entry point for launching an IPython kernel.\n"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize the histogram of the number of MOs of each simulation."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# figure(201)\ntotalMO = np.sum(isMO, axis=1)\nlth.plot_histogram(totalMO, r'MOs During Execution', np.array([0.1, 0.25, 0.5, 0.75, 0.9]), bins=np.arange(0,np.ceil(np.quantile(totalMO,0.999)),1) )",
"execution_count": 16,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Visualize the histogram of the inventory at the end of each simulation."
},
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "# figure(203)\nq = np.arange(0, Nq + 1, 1)\nmyn = np.full((Ndt + 1, Nq + 1), np.NaN)\nfor k in range(0, t.shape[0], 1):\n myn[k, :] = np.histogram(Qpath[:, k], bins=np.append(q, Nq + 1))[0]\nmyn = np.transpose(myn)\nmedq = np.median(Qpath, axis=0)\nmeanq = np.mean(Qpath, axis=0)\n\nlth.plot_heat_map(t=t, q=q, myn_per_sim=myn / Nsims, meanq=meanq, medq=medq, qAC=qAC, xlab=r'Time (sec)', ylab=r'Inventory',title=r'Inventory Heatmap')",
"execution_count": 17,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 2 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"name": "python",
"pygments_lexer": "ipython3",
"version": "3.5.4",
"file_extension": ".py",
"codemirror_mode": {
"version": 3,
"name": "ipython"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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