life_modeling_problem.ipynb

{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python38264bita04665306a3b44b794a2f52a43388ca8",
   "display_name": "Python 3.8.2 64-bit"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = np.array([0.001,0.002,0.003,0.003,0.004,0.004,0.005,0.007,0.009,0.011])\n",
    "w = np.array([0.05,0.07,0.08,0.10,0.14,0.20,0.20,0.20,0.10,0.04])\n",
    "P = 100\n",
    "S = 25000\n",
    "r = 0.02"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def npv(q,w,P,S,r):\n",
    "    decrements = np.cumprod(1-q-w)\n",
    "    inforce = np.empty_like(decrements)\n",
    "    inforce[:1] = 1\n",
    "    inforce[1:] = decrements[:-1]\n",
    "    ncf = inforce * P - inforce * q * S\n",
    "    t = np.arange(np.size(q))\n",
    "    d = np.power(1/(1+r), t)\n",
    "    return np.sum(ncf * d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "51.33132737013757"
      ]
     },
     "metadata": {},
     "execution_count": 54
    }
   ],
   "source": [
    "npv(q,w,P,S,r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "21 µs ± 553 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit npv(q,w,P,S,r)"
   ]
  }
 ]
}