{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear-Quadratic Model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demdp18.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-23\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## About\n", "\n", "Simple Linear-Quadratic control example. Illustrates use of lqsolve.\n", "\n", "States\n", "* s generic state of dimension ds=3\n", "\n", "Actions\n", "* x generic action of dimension dx=2" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import LQmodel, nodeunif\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## One-Dimensional Problem" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Input Model Parameters\n", "F0 = 0.0\n", "Fs = -1.0\n", "Fx = -0.0\n", "Fss = -1.0\n", "Fsx = 0.0\n", "Fxx = -0.1\n", "G0 = 0.5\n", "Gs = -0.2\n", "Gx = 0.5\n", "delta = 0.9\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve model using **LQmodel**" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'s': array([[-0.4528]]),\n", " 'x': array([[-2.0867]]),\n", " 'p': array([[-0.4637]]),\n", " 'v': array([[1.3257]])}" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = LQmodel(F0,Fs,Fx,Fss,Fsx,Fxx,G0,Gs,Gx,delta)\n", "model.steady" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "sstar, xstar, pstar, vstar = model.steady_state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot results" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "n, smin, smax = 100, -5, 5\n", "s = np.linspace(smin, smax, n)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "S = model.solution(s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimal policy and value function" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2)\n", "S['x'].plot(ax=axs[0])\n", "axs[0].set(title='Optimal Policy', xlabel='s', ylabel='x')\n", "\n", "S['value'].plot(ax=axs[1])\n", "axs[1].set(title='Value Function', xlabel='$s$', ylabel='Value');" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } }, "source": [ "## Higher Dimensional Problem" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "F0 = 3\n", "Fs = [1, 0]\n", "Fx = [1, 1]\n", "Fss = [[-7, -2],[-2, -8]]\n", "Fsx = [[0, 0], [0, 1]]\n", "Fxx = [[-2, 0], [0, -2]]\n", "G0 = [[1], [1]]\n", "Gs = [[-1, 1],[1, 0]]\n", "Gx = [[-1, -1],[2, 3]]\n", "delta = 0.95" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "model2 = LQmodel(F0,Fs,Fx,Fss,Fsx,Fxx,G0,Gs,Gx,delta)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "n = [8,8]\n", "ss = nodeunif(n,-1,1)\n", "S2 = model2.solution(ss)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def plot3d(y):\n", " s0 = S2['s0'].values.reshape(n)\n", " s1 = S2['s1'].values.reshape(n)\n", " z = S2[y].values.reshape(n)\n", " \n", " fig = plt.figure(figsize=[12, 6])\n", " ax = fig.add_subplot(1, 1, 1, projection='3d')\n", " ax.plot_surface(s0, s1, z, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", " ax.set_xlabel('$s_0$')\n", " ax.set_ylabel('$s_1$')\n", " ax.set_zlabel(y)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } }, "source": [ "### Value function" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot3d('value')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } }, "source": [ "### Optimal policy" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot3d('x0')\n", "plot3d('x1')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } }, "source": [ "### Simulations" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.6436]\n", " [-0.3275]]\n", "[[ 0.1272]\n", " [-0.7418]]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sini = model2.steady['s']/3\n", "\n", "data = model2.simulate(16,sini)\n", "data.set_index('time', inplace=True)\n", "\n", "data.plot(subplots=True,layout=(2,2), figsize=[9,4])\n", "print(model2.steady['s'])\n", "print(model2.steady['x'])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 2 }