{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#In-this-notebook,\" data-toc-modified-id=\"In-this-notebook,-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>In this notebook,</a></span></li><li><span><a href=\"#Expected-utility-via-Monte-Carlo\" data-toc-modified-id=\"Expected-utility-via-Monte-Carlo-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Expected utility via Monte Carlo</a></span><ul class=\"toc-item\"><li><span><a href=\"#Plotting-the-exact-solution\" data-toc-modified-id=\"Plotting-the-exact-solution-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Plotting the exact solution</a></span></li><li><span><a href=\"#MC-implementation\" data-toc-modified-id=\"MC-implementation-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>MC implementation</a></span></li></ul></li><li><span><a href=\"#Exercise\" data-toc-modified-id=\"Exercise-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Exercise</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 4. Expected utility and Monte Carlo in Python\n",
    "**Camilo A. Garcia Trillos - 2020**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## In this notebook,\n",
    "- we look at the Monte Carlo method and how to use it to approximate expected utilities or certainty equivalents.\n",
    "- we use Python to plot information using matplotlib, including a histogram and a regression\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us import some packages: math, numpy, matplotlib and scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from numpy.random import default_rng  #  pseudo-random number generator\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# This is an indicator to tell jupyter notebook to show us all plots inline:\n",
    "%matplotlib inline \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Expected utility via Monte Carlo\n",
    "\n",
    "To compute the expected utility of a wealth gamble $W$ we can use he law of large numbers. Indeed, if $E[|u(W)|]<\\infty$, we have\n",
    "$$  \\frac{1}{N} \\sum_{i=1}^N u(W_i)  \\rightarrow \\mathbb E[u(W)] \\text{ as } N\\rightarrow \\infty,$$\n",
    "where $(W_i)$ is a family of independent draws of random variables with $W_i \\sim W$ for each $i$.\n",
    "\n",
    "The Monte Carlo method relies on this equality to produce an approximation to the expectation (by choosing a large N and calculating the empirical average).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "To see how this works, let us start with $W$ being normally distributed, that is $W = \\sigma N + \\mu$, where $\\mu, \\sigma \\in \\mathbb R$ and $N$ is standard normally distributed.  \n",
    "\n",
    "Now, let us suppose first we want to compute expected utility of a CARA utility $u(x) = 1-\\exp(-\\alpha * x)$. We can calculate explicitly\n",
    "$$ \\mathbb E[u(W)] = \\mathbb E[1- \\exp(-\\alpha \\sigma N - \\alpha \\mu  ))] =1- \\exp\\left(-\\alpha \\mu + \\frac 1 2 \\alpha^2 \\sigma^2  \\right).$$\n",
    "\n",
    "We use this value to compare to the value approximated by Monte Carlo as explained before. Let us build a plot of this function in some given domain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Plotting the exact solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are several libraries allowing us to plot in Python. We will use one of the simplest: Matplotlib.\n",
    "\n",
    "A simple way to plot in this library is to provide it with vectors of input and output. To try it, let us simply plot the result of the (exact) expected utility when the CARA coefficient changes.\n",
    "\n",
    "We start by sampling the space of coefficients of risk aversion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e-03 3.12929293e-02 6.15858586e-02 9.18787879e-02\n",
      " 1.22171717e-01 1.52464646e-01 1.82757576e-01 2.13050505e-01\n",
      " 2.43343434e-01 2.73636364e-01 3.03929293e-01 3.34222222e-01\n",
      " 3.64515152e-01 3.94808081e-01 4.25101010e-01 4.55393939e-01\n",
      " 4.85686869e-01 5.15979798e-01 5.46272727e-01 5.76565657e-01\n",
      " 6.06858586e-01 6.37151515e-01 6.67444444e-01 6.97737374e-01\n",
      " 7.28030303e-01 7.58323232e-01 7.88616162e-01 8.18909091e-01\n",
      " 8.49202020e-01 8.79494949e-01 9.09787879e-01 9.40080808e-01\n",
      " 9.70373737e-01 1.00066667e+00 1.03095960e+00 1.06125253e+00\n",
      " 1.09154545e+00 1.12183838e+00 1.15213131e+00 1.18242424e+00\n",
      " 1.21271717e+00 1.24301010e+00 1.27330303e+00 1.30359596e+00\n",
      " 1.33388889e+00 1.36418182e+00 1.39447475e+00 1.42476768e+00\n",
      " 1.45506061e+00 1.48535354e+00 1.51564646e+00 1.54593939e+00\n",
      " 1.57623232e+00 1.60652525e+00 1.63681818e+00 1.66711111e+00\n",
      " 1.69740404e+00 1.72769697e+00 1.75798990e+00 1.78828283e+00\n",
      " 1.81857576e+00 1.84886869e+00 1.87916162e+00 1.90945455e+00\n",
      " 1.93974747e+00 1.97004040e+00 2.00033333e+00 2.03062626e+00\n",
      " 2.06091919e+00 2.09121212e+00 2.12150505e+00 2.15179798e+00\n",
      " 2.18209091e+00 2.21238384e+00 2.24267677e+00 2.27296970e+00\n",
      " 2.30326263e+00 2.33355556e+00 2.36384848e+00 2.39414141e+00\n",
      " 2.42443434e+00 2.45472727e+00 2.48502020e+00 2.51531313e+00\n",
      " 2.54560606e+00 2.57589899e+00 2.60619192e+00 2.63648485e+00\n",
      " 2.66677778e+00 2.69707071e+00 2.72736364e+00 2.75765657e+00\n",
      " 2.78794949e+00 2.81824242e+00 2.84853535e+00 2.87882828e+00\n",
      " 2.90912121e+00 2.93941414e+00 2.96970707e+00 3.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0.001,3,100) # creates a vector of size 100 with numbers between 0.1 and 30\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We now implement the exact solution expected CARA utility under normal assumptions. Since it is a simple expression, we can use a lambda function as introduced before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# The operations in expected_u are well defined for vectors as long as mu,sd,x broadcast correctly together.\n",
    "expected_u = lambda mu,sigma,alpha: 1-np.exp(-alpha*mu+0.5*alpha**2*sigma**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Note that we use 'np.exp' and not 'math.exp': this is because we want the function to be 'vectorial', that is, to accept vectors as an input \n",
    "\n",
    "(try changing np.exp for math.exp, run the code and then run the code below... there will be an error)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.98553078e-03  1.43161779e-01  2.59436323e-01  3.57578415e-01\n",
      "  4.40665016e-01  5.11214871e-01  5.71295417e-01  6.22608244e-01\n",
      "  6.66557592e-01  7.04305396e-01  7.36815622e-01  7.64890079e-01\n",
      "  7.89197408e-01  8.10296616e-01  8.28656217e-01  8.44669848e-01\n",
      "  8.58669036e-01  8.70933653e-01  8.81700514e-01  8.91170449e-01\n",
      "  8.99514138e-01  9.06876943e-01  9.13382902e-01  9.19138057e-01\n",
      "  9.24233215e-01  9.28746256e-01  9.32744058e-01  9.36284107e-01\n",
      "  9.39415849e-01  9.42181820e-01  9.44618597e-01  9.46757599e-01\n",
      "  9.48625755e-01  9.50246068e-01  9.51638082e-01  9.52818282e-01\n",
      "  9.53800408e-01  9.54595733e-01  9.55213272e-01  9.55659954e-01\n",
      "  9.55940751e-01  9.56058773e-01  9.56015322e-01  9.55809920e-01\n",
      "  9.55440295e-01  9.54902345e-01  9.54190056e-01  9.53295395e-01\n",
      "  9.52208157e-01  9.50915768e-01  9.49403046e-01  9.47651906e-01\n",
      "  9.45640992e-01  9.43345252e-01  9.40735416e-01  9.37777378e-01\n",
      "  9.34431459e-01  9.30651531e-01  9.26383973e-01  9.21566425e-01\n",
      "  9.16126303e-01  9.09979026e-01  9.03025898e-01  8.95151561e-01\n",
      "  8.86220947e-01  8.76075607e-01  8.64529284e-01  8.51362567e-01\n",
      "  8.36316424e-01  8.19084342e-01  7.99302784e-01  7.76539543e-01\n",
      "  7.50279522e-01  7.19907310e-01  6.84685798e-01  6.43729854e-01\n",
      "  5.95973852e-01  5.40131507e-01  4.74646078e-01  3.97628461e-01\n",
      "  3.06780053e-01  1.99296367e-01  7.17463012e-02 -8.00794903e-02\n",
      " -2.61359526e-01 -4.78482558e-01 -7.39352719e-01 -1.05377686e+00\n",
      " -1.43395752e+00 -1.89512203e+00 -2.45632757e+00 -3.14149420e+00\n",
      " -3.98073414e+00 -5.01206692e+00 -6.28363866e+00 -7.85660183e+00\n",
      " -9.80886243e+00 -1.22399700e+01 -1.52775168e+01 -1.90855369e+01]\n"
     ]
    }
   ],
   "source": [
    "sd, mu = 2,5  # Equivalently sd=2 and mu=5\n",
    "y=expected_u(mu,sd,x) # Note that x is a vector\n",
    "print(y) # And so is y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "If for some reason you cannot implement directly a vectorial function, it is possible to use a loop or the function np.vectorize to render the function vector ready."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We are ready to make the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Expected utility')"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 521
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(x,y)   # Make a plot between x and y\n",
    "plt.title('Expected utility as a function of coefficient of absolute risk aversion - Gaussian case') # Add a title\n",
    "plt.xlabel('Coefficient of risk aversion') # Add a label on the x axis\n",
    "plt.ylabel('Expected utility') # Add a label on the y axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### MC implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us now look at the Monte Carlo approximation of the above function. We start by defining a function that calculates the CARA utility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
   ],
   "source": [
    "cara_utility = lambda x,alpha: 1-np.exp(-alpha*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Some tests on our function\n",
    "assert cara_utility(1,1)== 1-1./math.e , \"Failed test with x=1, alpha =1\"\n",
    "assert cara_utility(5,2)== 1-math.e**-10., \"Failed test with x=5, alpha=2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can now generate a sample of wealths, distributed like a $\\mathcal N (\\mu,\\sigma^2)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "sd, mu = 2,5  # Equivalently sd=2 and mu=5\n",
    "N = 10000\n",
    "rng = default_rng()\n",
    "sample_gaussian = rng.normal(mu,sd,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "How can we check that these are Gaussian? We can plot the histogram of the empirical distribution defined. The package matplotlib has a convenient function for this: *plt.hist* (recall that plt is our alias for pyplot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'density')"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 398
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.hist(sample_gaussian, density=True)  # Plots the histogram, normalising to obtain a pdf.\n",
    "plt.title('Histogram of our sample') # Add a title to the plot\n",
    "plt.xlabel('sample_gaussian') # Add a label on the X axis\n",
    "plt.ylabel('density') # Add a label on the Y axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "It looks like a good Gaussian sample with our parameters (centred in 5 and with standard deviation 2). In later notebooks we will learn some alternative ways for checking Gaussianity. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can now calculate a Monte Carlo approximation of our expected utility. Examine the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9549462281514323"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cara_utility(sample_gaussian,1).mean()  # In one line, we evaluate the cara utility for each entry of the sample, and then calculate the mean of the resulting vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Observe now the following: the estimation is random. To see this, let us run the estimation with another sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9539255937674046"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cara_utility(rng.normal(mu,sd,N),1).mean()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As expected, the two values are close but different. Indeed, this estimator is **random**, because it depends on the sample, which is itself random. This is something to be taken into account when using Monte Carlo estimators. \n",
    "\n",
    "In fairness, the Python implementation of the MC estimator can only produce a pseudo-random generation. To see this, we can fix the seed of the pseudo-random generation algorithm and compare the answers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "rng = default_rng(1234)\n",
    "sample_gaussian = rng.normal(mu,sd,N)\n",
    "mc_eu1 = cara_utility(sample_gaussian,1).mean()\n",
    "rng = default_rng(1234)\n",
    "sample_gaussian2 = rng.normal(mu,sd,N)\n",
    "mc_eu2 = cara_utility(sample_gaussian2,1).mean()\n",
    "print(mc_eu1-mc_eu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Setting the random states allows us to repeat the same sequence on the pseudo-random generation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Now, let us remind ourselves of the closed form solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.950212931632136"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_u(mu,sd,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We see that the value is very close to the value(s) estimated via MC. Indeed, this error can be explained via the central limit theorem, which give us a control on the L_2 norm and is of the form\n",
    "\n",
    "$$\\left \\|\\mathbb E[u(W)] - \\frac 1 N \\sum_{i=1}^N u(W_i)    \\right \\|_{L_2} \\leq \\frac{C}{N^{1/2}} {\\rm sd}(X_1)  $$\n",
    "\n",
    "Let us verify this empirically, using a plot and a regression. We want to retrieve the rate of convergence, which is the power 1/2 in the above control. To do this we use a log-log plot (think why)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f12148bef70>"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 278,
       "width": 517
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_vec = 2**np.arange(10,20) # The number of MC simulations, we take powers of 2\n",
    "rng = default_rng(1) # Fix the seed to \"1\", so that the plot looks the same every time you run it\n",
    "u = np.array([cara_utility(rng.normal(mu,sd,N),1).mean() for N in n_vec])  # Create an MC expected utility for the sizes above\n",
    "error = np.abs(u - expected_u(mu, sd, 1)) # Calculate the error\n",
    "plt.loglog(n_vec, error, 'ro', label='Error') # Make a log log plot\n",
    "plt.title('Error in Monte Carlo Expected utility as a function of size of sample - Gaussian case')\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('Error')\n",
    "\n",
    "# Let us also add a reference line. To do so, we need to calculate a simple regression. We can use the polyfit function\n",
    "m, b = np.polyfit( np.log(n_vec), np.log(error), 1)\n",
    "plt.loglog(n_vec, np.exp(b+m*np.log(n_vec)), 'g--', label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The hardest line of code in the plot above is possibly\n",
    "```python\n",
    "plt.loglog(n_vec, np.exp(b+m*np.log(n_vec)), 'g--', label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "```\n",
    "\n",
    "Let us look at two parts in particular:\n",
    "\n",
    "```python\n",
    "'g--'\n",
    "```\n",
    "Means make a green dashed line.\n",
    "\n",
    "while \n",
    "```python\n",
    "label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "```\n",
    "means: take the value of exp(b), round it to a float with two decimal figures, do the same with m, and write a string that contains exp(b) N^ m with this format. This is saved on a variable label that is used by matplotlib to assign the legends in a plot.\n",
    "\n",
    "Check that you understand the other lines of code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Note that the best fit slope is close to -1/2 as expected. This is consistent with the theoretical error given before. **Write the equations to be sure you understand why.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercise\n",
    "\n",
    "1. Compute, via a Monte-Carlo simulation, the expected utility of a CRRA investor for the following gambles.\n",
    "    - $W_1 \\sim |aN + b|$, where $N$ is standard normally distributed and $a,b \\in R$.\n",
    "    - $W_2 \\sim \\text{Exp}(\\lambda_2)$ where $\\lambda_2>0$.\n",
    "\t\n",
    "You might have to look up online the commands for the corresponding random number generators. (Use the ones in numpy.random)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# We first implement the CRRA utility function\n",
    "\n",
    "\n",
    "def crra(x,rho=1):\n",
    "    if rho==1:\n",
    "        return np.log(x)\n",
    "    else:\n",
    "        return (x**(1-rho))/(1-rho)\n",
    "\n",
    "    \n",
    "assert crra(5,1)== np.log(5)\n",
    "assert crra(5,2)== -1/5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected utility of $W_1$ is  -1.5481311223192271\n",
      "The expected utility of $W_2$ is  -5.875820936362287\n",
      "The investor will choose $W_1$\n"
     ]
    }
   ],
   "source": [
    "# We include here the number of MC simulations and the coeff. of relative risk aversion\n",
    "\n",
    "num_samples = 10000\n",
    "rho = 2\n",
    "\n",
    "\n",
    "# W_1\n",
    "\n",
    "a = 1\n",
    "b = 2\n",
    "w1 = np.abs(a*rng.standard_normal(num_samples)+b)\n",
    "u1 = crra(w1,rho).mean()\n",
    "print('The expected utility of $W_1$ is ', u1)\n",
    "\n",
    "# W_2\n",
    "\n",
    "mlambda = 0.5 # This is the rate parameter\n",
    "\n",
    "w2 = rng.exponential(1/mlambda, num_samples)   # Note that the generator receives 1/lambda\n",
    "u2 = crra(w2,rho).mean()\n",
    "print('The expected utility of $W_2$ is ', u2)\n",
    "if u2>u1:\n",
    "    print('The investor will choose $W_2$')\n",
    "else:\n",
    "    print('The investor will choose $W_1$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram for $W_1$')"
      ]
     },
     "execution_count": 49,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 49,
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.hist(w1, density=True)\n",
    "plt.title('Histogram for $W_1$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram for $W_2$')"
      ]
     },
     "execution_count": 51,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 51,
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.hist(w2, density=True)\n",
    "plt.title('Histogram for $W_2$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "rng.exponential?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "2. Write a function that computes the certainty equivalent for a CRRA investor. (Hint: You might have to compute, on a piece of paper, $u^{-1}$ for the different relative risk aversions $\\rho$.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected utility of $W_1$ is  0.6459401181095812\n",
      "The expected utility of $W_2$ is  0.17018898479556094\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def ce_crra(x,rho):\n",
    "    eu = crra(x,rho).mean()\n",
    "    if rho==1:\n",
    "        return np.exp(eu)\n",
    "    else:\n",
    "        return ((1-rho)*eu)**(1/(1-rho))\n",
    "\n",
    "\n",
    "assert crra(ce_crra(w1,rho),rho)==u1,'Failed test with W1'\n",
    "assert crra(ce_crra(w2,rho),rho)==u2,'Failed test with W2'\n",
    "    \n",
    "    \n",
    "    \n",
    "print('The expected utility of $W_1$ is ', ce_crra(w1,rho))\n",
    "print('The expected utility of $W_2$ is ', ce_crra(w2,rho))\n",
    "\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "3. With $a = 1$ and $b = 2$, plot the certainty equivalent of a CRRA investor as a function of relative risk aversion $\\rho$, using gamble $W_1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Certainty equivalent')"
      ]
     },
     "execution_count": 47,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 47,
     "metadata": {
      "image/png": {
       "height": 278,
       "width": 417
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "rho_vec = np.arange(0.01,5,0.1)\n",
    "ce_vec = np.array([ce_crra(w1,rho) for rho in rho_vec])\n",
    "\n",
    "plt.plot(rho_vec,ce_vec)\n",
    "plt.title('Certainty equivalent of $W_1$ as a function of relative risk aversion')\n",
    "plt.xlabel('Relative risk aversion')\n",
    "plt.ylabel('Certainty equivalent')\n",
    "\n"
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    "The plot shows that the certainty equivalent decreases quickly as a function of the relative risk aversion. This is to be expected: as the coefficient of relative risk aversion increases, we are willing to exchange the risk in the distribution for only a small secure amount."
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