#!/usr/bin/env python
# coding: utf-8

# # Example: Asset Replacement

# Miranda and Fackler, Applied Computational Economics and Finance, 2002, Section 7.6.2

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get_ipython().run_line_magic('matplotlib', 'inline')


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from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
from quantecon.markov import DiscreteDP


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n = 5  # Number of states
m = 2  # Number of actions; 0: keep, 1: replace
repcost = 75  # Replacement cost
beta = 0.9  # Discount factor


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# Reward array
R = np.empty((n, m))
S = np.arange(n) + 1
R[:, 0] = 50 - 2.5 * S - 2.5 * S**2
R[:, 1] = 50 - repcost

# Infeasible action
R[-1, 0] = -np.inf


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R


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# (Degenerate) transition probability array
Q = np.zeros((n, m, n))
for i in range(n):
    Q[i, 0, np.minimum(i+1, n-1)] = 1
    Q[i, 1, 0] = 1


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Q


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# Create a DiscreteDP
ddp = DiscreteDP(R, Q, beta)


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# Solve the dynamic optimization problem (by policy iteration)
res = ddp.solve()


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# Number of iterations
res.num_iter


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# Optimal value function
res.v


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# Optimal policy
res.sigma


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# Transition probability matrix
res.mc.P


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# Simulate the controlled Markov chain
initial_state = 0
ts_length = 13
age_path = res.mc.simulate(ts_length=ts_length, init=initial_state) + 1


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fig, ax = plt.subplots(1, 2, figsize=(12, 4))
ax[0].plot(np.arange(n)+1, res.v)
ax[0].set_xticks(np.linspace(1, 5, 5, endpoint=True))
ax[0].set_xlabel('Age of Machine')
ax[0].set_ylabel('Value')
ax[0].set_title('Optimal Value Function')

ax[1].plot(age_path)
ax[1].set_yticks(np.linspace(1, 4, 4, endpoint=True))
ax[1].set_xlabel('Year')
ax[1].set_ylabel('Age of Machine')
ax[1].set_title('Optimal State Path')

plt.show()


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