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Solving the competitive storage model using collocation
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solving the competitive storage model using Python\n",
"\n",
"Author: [Jyotirmoy Bhattacharya](https://www.jyotirmoy.net)\n",
"Date: December 26, 2015"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This IPython notebook solves the competitive storage model for the price of storable commodities using collocation as the numerical method. We reproduce an example from section 9.9.2 of Miranda and Fackler's *Applied Computational Economics and Finance* using Python and independently of the authors' CompEcon MATLAB toolbox."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The problem\n",
"\n",
"The competitive storage model is a simple model for the price of a storable commodity. It has an uneven empirical record but it provides a good illustration of the computational problems which arise in modern macroecnomics. \n",
"\n",
"We consider a commodity, say wheat, which can be stored subject to the condition that a fraction $\\lambda$ of the total stock at the end of a period disappears before the beginning of the next period and a cost per unit cost $c$ has to be paid for storage. In each period there is an addition to stocks due to a stochastic harvest $z$ and a reduction in stock from an outside demand given by a demand function $P(q)$. \n",
"\n",
"Storage decisions are taken by competitive speculators who must form expectations about future prices. These future prices depend on both the stochastic harvest in the next period as well as the total stock carried forward by all speculators taken together. We assume that speculators have rational expectations.The speculators are assumed to be risk neutral and discount their future profits by a discount factor $\\delta$.\n",
"\n",
"Let $s_t$ be the stock at the beginning of period $t$ and $x_t$ be the stock at the end of period $t$ and $p_t$ be the price that prevails in period $t$. Then the equilibrium conditions are, first that outside consumers should demand the quantity $(s_t-x_t)$ that is not stored,\n",
"\n",
"$$p_t = P(s_t-x_t)$$\n",
"\n",
"that the stocks in consecutive periods be linked according to the storage technology,\n",
"$$s_{t+1} = (1-\\lambda)x_t+z_{t+1}$$\n",
"\n",
"and most importantly the speculators maximize profits.\n",
"$$p_t \\ge \\delta(1-\\lambda)[E_t p_{t+1}]-c,\\quad \\text{with equality if $x_t>0$}$$\n",
"\n",
"The last equation has the complementary slackness form it has becuase speculators may be at a corner solution where they do not carry forward any stocks at all. If this is the case then current prices can rise above the expected future return from carrying stocks. On the other hand current prices can never be lower than expected revenues from storage in equilibrium since such a condition would produce an infinite demand for wheat by speculators in the current period."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The solution algorithm\n",
"\n",
"[It is known](http://www.jstor.org/stable/2297923) that the above system of equations has a solution of the form $p_t = \\phi(s_t)$. However there is generally no analytical solution and the function $\\phi(\\cdot)$ must be computed numerically.\n",
"\n",
"Suppose we expect that prices next period are governed by the function $f(s_{t+1})$. Then the price function this period, say $g(s_{t})$, will be a function of this expectation through our equilibrium conditions above. We express this relationship in the form\n",
"\n",
"$$g = Tf$$\n",
"\n",
"where $T$ is an abstract operator representing the working of the equilibrium conditions. It is precisely the property of a stationary rational equations solution that it is a fixed-point of this operator\n",
"\n",
"$$\\phi = T\\phi$$\n",
"\n",
"i.e., the expected law of prices is such as to produce behaviour which confirms the expect law of prices.\n",
"\n",
"In order to find an approximate solution to this fixed-point equation we restrict our search to the finite dimensional space of [Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials) of a given degree. The true solution may not lie in this space and thus no function in this space may satisfy the fixed-point equation at all points. In order to nonetheless get a good approximation to the true solution the collocation method we use in this notebook requires that the function come close to satising the fixed-point equation at a given finite set of points. In this notebook we take these points to be [Chebyshev nodes](https://en.wikipedia.org/wiki/Chebyshev_nodes). The task of finding the Chebyshev polynomial which satisfies this condition is carried out through successive approximation: starting from an initial guess $f_0$ we calculate $y_n = (Tf_0)(x_n)$ at our chosen Chebyshev nodes $x_n$. Then $f_1$ is then taken to be a Chebyshev polynomial that passes through the points $(x_n,y_n)$. This is continued until we reach a fixed point.\n",
"\n",
"There are two more technical difficulties. The operator $T$ involves computing a conditional expectation in order to find expected profits. For arbitrary functions this cannot be done exactly and we have to make a numerical approximation. In this notebook we use [Gauss-Hermite quadrature](https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature) to replace the continuous distribution of the shocks $z_t$ by a discrete approximation.\n",
"\n",
"Finally, we need to work with a bounded state space for our calculations. If $\\lambda>0$ and $\\bar z$ the maximum possible realization of the shock then the beginning-of-period stock can never exceed $\\bar z/\\lambda$. This however does not work when $\\lambda=0$. Also using this bound is harmful even when $\\lambda>0$ since this forces us to consider very large values of stock which are not reached in equilibrium, thereby wasting computational resources. We therefore follow the literature in arbitrarily assuming that there is an upper abound $x_{max}$ on end-of-period stocks. The value of this parameter is adjusted to be large enought that it is never reached in equilibrium.\n",
"\n",
"See Judd, *Numerical Methods in Economics*, Chapter 11 and 17 for more details as well as alternative algorithms. Section 17.4 discusses the competitive storage model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import sys\n",
"import math as m\n",
"import numpy as np\n",
"from numpy import linalg\n",
"import scipy.optimize as spopt\n",
"from numpy.polynomial.chebyshev import Chebyshev\n",
"from numpy.polynomial.hermite import hermgauss\n",
"from scipy.stats import rv_discrete\n",
"import scipy.io as spio\n",
"import matplotlib.pyplot as plt\n",
"from collections import namedtuple\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Collocation\n",
"\n",
"## Collocation in general"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def collocation_solve(T,fhat,nodes,fit,log=True,tol=1e-6,maxiter=500):\n",
" \"\"\"\n",
" Try to solve the operator equation Tf = f.\n",
" We use successive approximations to find a function fhat in some function\n",
" space such that Tfhat = fhat at all points in `nodes`.\n",
" \n",
" Inputs:\n",
" \n",
" T(fhat,s): return (Tfhat)(s)\n",
" fhat: initial guess for fhat\n",
" nodes: collocation nodes\n",
" fit: a function when called as fit(x,y) with x and y \n",
" as arrays, returns an element phi of the chosen\n",
" function space such that phi(x[i]) = y[i]\n",
" log: if True prints progress messages\n",
" tol: tolerance parameter for stopping criteria\n",
" maxiter: maximum number of successive approximation \n",
" iterations to try\n",
" \n",
" Returns:\n",
" \n",
" Either `fhat` if success or `None` if iteration count exceeded.\n",
" \"\"\"\n",
" \n",
" for i in range(maxiter):\n",
" lhs = np.empty_like(nodes)\n",
" rhs = np.empty_like(nodes)\n",
" for j,s in enumerate(nodes):\n",
" lhs[j] = T(fhat,s)\n",
" rhs[j] = fhat(s)\n",
" err = linalg.norm(lhs-rhs,np.inf)\n",
" if log and i%10==0:\n",
" print(\"Iteration {}: Error = {:.2g}\".format(i+1,err),\n",
" file=sys.stderr)\n",
" plt.plot(nodes,lhs,\"b-\",label=\"Tf\")\n",
" plt.plot(nodes,rhs,\"r-\",label=\"f\")\n",
" plt.legend()\n",
" plt.show()\n",
" fhat = fit(nodes,lhs)\n",
" if err<tol:\n",
" return fhat\n",
" if log:\n",
" print(\"collocation_solve: iteration count exceeded\",file=sys.stderr)\n",
" return None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Collocation using Chebyshev polynomials and nodes"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def chebyshev_solve(T,guesser,degree,domain,log=True,tol=1e-6,maxiter=500):\n",
" \"\"\"\n",
" Try to solve the operator equation Tf = f using\n",
" Chebychev collocation.\n",
" \n",
" \n",
" Inputs:\n",
" \n",
" T(fhat,s): return (Tfhat)(s)\n",
" guesser: a function, `guesser(x)` gives a guess for the function\n",
" at point `x`.\n",
" degree: the degree of the Chebyshev series to use\n",
" domain: a list `[lower,upper]` of the domain over which the function\n",
" is to be approximated\n",
" log: if True prints progress messages\n",
" tol: tolerance to be used in stopping criteria\n",
" maxiter: maximum number of iterations for successive approximation.\n",
" \n",
" Returns:\n",
" Either `fhat` if success or `None` if iteration count exceeded.\n",
" \"\"\"\n",
" \n",
" nodes = Chebyshev.basis(degree+1,domain).roots()\n",
" \n",
" def fitter(x,y):\n",
" return Chebyshev.fit(x,y,degree,domain)\n",
" \n",
" f0 = fitter(nodes,\n",
" np.array([guesser(n) for n in nodes]))\n",
" \n",
" return collocation_solve(T,f0,nodes,fitter,log,tol,maxiter)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The competitive storage model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The problem data structure"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# A competitive storage problem\n",
"StorageProb = namedtuple(\"StorageProb\",\n",
" [\"cost\" # Marginal cost per-unit stored\n",
" ,\"shrink\" # Fraction of goods lost per period ($\\lambda$)\n",
" ,\"yvol\" # Log of harvest is distributed N(0,yvol)\n",
" ,\"xmax\" # Maximum end-of-period stock\n",
" ,\"disc\" # Time discount rate ($\\delta$)\n",
" ,\"P\" # External demand function P(q)\n",
" ])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Solving the problem\n",
"class StorageSolution(object):\n",
" \"\"\"\n",
" A solution to the competitve storage model.\n",
" \n",
" Constructor:\n",
" \n",
" StorageSolution(prob,hgdeg=5,cdeg=50,tol=1e-6,maxiter=500,log=True)\n",
" \n",
" hgdeg: degree of Gauss-Hermite discretization of shocks\n",
" cdeg: dgree of Chebychev polynomial to use\n",
" tol: tolerance for stopping criteria\n",
" maxiter: maximum no of iterations \n",
" log: if True print progress report\n",
" \n",
" The model is solved in the process of constructing the object,\n",
" so constructor calls are expensive.\n",
" \n",
" If the model cannot be solved in the give number of iterations\n",
" throws a ValueError. Computational problems can cause an\n",
" AssertionError to be thrown.\n",
" \n",
" Instance variables:\n",
" \n",
" Saved from constructor: prob, hgdeg, cdeg, tol\n",
" \n",
" Others:\n",
" \n",
" smax Maximum beginning-of-period stock\n",
" smin Minimum beginning-of-period stock\n",
" zs An array of discretized harvest shock values\n",
" ws An array of probability weights corresponding to `ws`\n",
" \n",
" phi The computed price as a function of begining-of-period shocks\n",
" \n",
" storage_revenue(phi,x)\n",
" Discounted expected revenue net of storage costs per unit stored\n",
" when the pricing function is `phi` and end-of-period stocks in the\n",
" current period is `x`.\n",
" \n",
" opti_storage(phi,s)\n",
" The optimal amount to store when the pricing function is `phi`\n",
" and beginning-of-period stocks is `s`. Rational expectations is\n",
" built in: the expected stocks tomorrow is consistent with storage\n",
" decision taken.\n",
" T(phi) We want T(phi,s) = phi(s) for all s.\n",
" \"\"\"\n",
" \n",
" def __init__(self,p,ghdeg=5,cdeg=50,tol=1e-6,maxiter=500,log=True):\n",
" \n",
" # Store input parameters\n",
" self.prob = p\n",
" self.ghdeg = ghdeg\n",
" self.cdeg = cdeg\n",
" self.tol = tol\n",
" \n",
" # Compute Gauss-Hermition integration nodes\n",
" ys,self.ws = hermgauss(ghdeg)\n",
" self.ws = self.ws/m.sqrt(m.pi)\n",
" self.zs = np.exp(ys*p.yvol)\n",
" zmin,zmax = np.min(self.zs), np.max(self.zs)\n",
" \n",
" # Bounds for beginning-of-period stocks\n",
" # Note xmax is maximum end-of-period shocks\n",
" self.smin = zmin\n",
" self.smax = zmax + (1 - p.shrink)*p.xmax\n",
" \n",
" # Storage revenue computation\n",
" def storage_revenue(phi,x):\n",
" Etom = sum(\n",
" phi(z + (1 - p.shrink)*x)*w \n",
" for (z,w) in zip(self.zs,self.ws)\n",
" )\n",
" return p.disc*(1 - p.shrink)*Etom - p.cost\n",
" \n",
" self.storage_revenue = storage_revenue\n",
" \n",
" # Optimal storage decision\n",
" def opti_storage(phi,s):\n",
" P = p.P\n",
" xmax = p.xmax\n",
" \n",
" if s>xmax and storage_revenue(phi,xmax) > P(s-xmax):\n",
" return xmax\n",
" elif storage_revenue(phi,0) < P(s-0):\n",
" return 0\n",
" else:\n",
" max_feas = min(xmax,s)\n",
" x_star,r = spopt.brentq(lambda x:storage_revenue(phi,x)-P(s-x),\n",
" 0,max_feas,\n",
" full_output=True,\n",
" xtol=1e-5)\n",
" assert r.converged\n",
" return x_star\n",
" \n",
" self.opti_storage = opti_storage\n",
" \n",
" # Initial guess for pricing function\n",
" def init(s):\n",
" return p.P(s)\n",
" \n",
" # We want T(phi) = phi\n",
" def T(phi,s):\n",
" x_star = opti_storage(phi,s)\n",
" ans = p.P(s-x_star)\n",
" assert ans>=0\n",
" return ans\n",
" self.T = T\n",
" \n",
" self.phi = chebyshev_solve(T,init,cdeg,\n",
" [self.smin,self.smax],\n",
" log,tol,maxiter)\n",
" if self.phi is None:\n",
" raise ValueError(\"Failed to converge\")\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visualization and simulation"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def illustrate(soln):\n",
" \"\"\"\n",
" Plot solution variables and diagnostics\n",
" ``soln` is an instance of `StorageSolution`\n",
" \"\"\"\n",
" f,((ax1,ax2),(ax3,ax4)) = plt.subplots(2,2,sharex=True)\n",
" f.set_size_inches(10,10)\n",
" \n",
" ss = np.linspace(soln.smin,soln.smax,100)\n",
" \n",
" store = [soln.opti_storage(soln.phi,s) for s in ss]\n",
" ax1.plot(ss,store)\n",
" ax1.set_title(\"Equilibrium storage\")\n",
" ax1.set_xlabel(\"Supply\")\n",
" ax1.set_ylabel(\"Storage\")\n",
" \n",
" P = [soln.prob.P(s) for s in ss]\n",
" phi = [soln.phi(s) for s in ss]\n",
" ax2.plot(ss,P,\"r-\",label=\"without storage\")\n",
" ax2.plot(ss,phi,\"b-\",label=\"with storage\")\n",
" ax2.legend()\n",
" ax2.set_title(\"Equilibrium price\")\n",
" ax2.set_xlabel(\"Supply\")\n",
" ax2.set_ylabel(\"Price\")\n",
" \n",
" def optimal_profit(s):\n",
" x = soln.opti_storage(soln.phi,s)\n",
" return soln.storage_revenue(soln.phi,x)-soln.prob.P(s-x)\n",
" profits = [optimal_profit(s) for s in ss]\n",
" ax3.plot(ss,profits)\n",
" ax3.set_title(\"Arbitrage profit\")\n",
" ax3.set_ylabel(\"Profit\")\n",
" ax3.set_xlabel(\"Supply\")\n",
" \n",
" resid = [soln.T(soln.phi,s)-soln.phi(s) for s in ss]\n",
" ax4.plot(ss,resid)\n",
" ax4.set_title(\"Approximation residual\")\n",
" ax4.set_ylabel(\"Tf-f\")\n",
" ax4.set_xlabel(\"Supply\")\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def simulate(soln,niter,burnin=1000,s0=None):\n",
" \"\"\"\n",
" Run a simulation.\n",
" \n",
" soln: An instance of `Storage Solution`\n",
" niter: The number of iteration for which to return results\n",
" burnin: The number of initial iterations to discard\n",
" s0: Initial beginning-of-period stock. \n",
" None selects the middle point of the domain.\n",
" \n",
" Returns: arrays x and P of end-of-period stocks and prices\n",
" \n",
" \"\"\"\n",
" \n",
" xs = np.empty(niter)\n",
" Ps = np.empty(niter)\n",
" \n",
" if s0 is None:\n",
" s = (soln.smin+soln.smax)/2\n",
" elif s0 > soln.smax:\n",
" s = soln.smax\n",
" elif s0 < soln.smin:\n",
" s = soln.smin\n",
" else:\n",
" s = s0\n",
" \n",
" dist=rv_discrete(values=(range(len(soln.ws)),soln.ws))\n",
" phi = soln.phi\n",
" opti_storage = soln.opti_storage\n",
" shrink = soln.prob.shrink\n",
" zs = soln.zs\n",
" P = soln.prob.P\n",
" \n",
" for i in range(niter+burnin):\n",
" x = opti_storage(phi,s)\n",
" z = zs[dist.rvs(size=1)]\n",
" if i>burnin:\n",
" xs[i-burnin] = x\n",
" Ps[i-burnin] = P(s-x)\n",
" s = (1-shrink)*x+z\n",
" return xs,Ps"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example from Miranda & Fackler"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def isoelastic_demand(gamma):\n",
" return lambda q: q**(-gamma)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Iteration 1: Error = 0.14\n"
]
},
{
"data": {
"image/png": 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/v3iydemJ1/75ea1aReea+BIU3iISWQ4dKg7ykhOvS87P27/f9eD9Yd627enz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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4760fd5da0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Iteration 11: Error = 1.6e-08\n"
]
},
{
"data": {
"image/png": 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TsvfJviTP6TgiEsB0nHeAWfmN58h+/l5s/gekzcp0Oo6IBKg+H+dtjHnWGFNhjPn0JGMe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\nLjXG7AYagYV+Ty0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"text/plain": [
"<matplotlib.figure.Figure at 0x7f4760fd5cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Example from section 9.9.2 of Miranda & Fackler\n",
"mirfac_p = StorageProb(cost = 0.1,\n",
" shrink = 0,\n",
" P = isoelastic_demand(2.0),\n",
" yvol = 0.2,\n",
" xmax = 0.9,\n",
" disc = 0.9)\n",
"mirfac_s = StorageSolution(mirfac_p,tol=1e-10)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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LlnDrrdCrV/FeyxIzJ+NABpVK72PFokM2zsyYMGJ7ZRpjil2fPpCYCA884HUk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DNmaYFZWzNmucCs3BmZIllQYJZH48tEpJb161c8Y5abmVnuGLNigVn37mGMW6mBWbkZMwVm0hko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\nHJiZmZmZlcT/A4mDAtH2XC71AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4760fd5470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"illustrate(mirfac_s)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Proportion of stockouts = 0.71\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f475ed685c0>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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sjQ42X2HBa0Y25rWk5o6gbJg7Ii+i7EOO0nPXeFE7MlOyg/y08rkKXqzTlaJ0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\nS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pLsujSAqvz28pk7/tHRMpaXt6zRx+Rc71rwo6bedrCzL0A7fPv7xp2+e9+pYIrw6Dfz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\nEyx4MQzDMAzDbBP/P4inAu3F0TiuAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f475ef1b358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sim_N = 500\n",
"sim_xs,sim_Ps = simulate(mirfac_s,sim_N)\n",
"\n",
"print(\"Proportion of stockouts = {}\".format(1-float(np.count_nonzero(sim_xs))/sim_N))\n",
"f,(ax1,ax2) = plt.subplots(2,1,sharex=True)\n",
"f.set_size_inches(10,9)\n",
"ax1.plot(sim_xs,linewidth=0.3,color=\"orange\")\n",
"ax1.set_title(\"End of period stocks\")\n",
"ax2.plot(sim_Ps,linewidth=0.3,color=\"darkblue\")\n",
"ax2.set_title(\"Price\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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