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

# # DiscreteDP Example: Asset Replacement

# **Daisuke Oyama**
# 
# *Faculty of Economics, University of Tokyo*

# From Miranda and Fackler, <i>Applied Computational Economics and Finance</i>, 2002,
# Section 7.6.2

# In[1]:


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


# In[2]:


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


# In[3]:


maxage = 5    # Maximum asset age
repcost = 75  # Replacement cost
beta = 0.9    # Discount factor
m = 2         # Number of actions; 0: keep, 1: replace


# In[4]:


S = np.arange(1, maxage+1)  # State space
n = len(S)                  # Number of states


# In[5]:


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

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


# In[6]:


R


# In[7]:


# (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


# In[8]:


Q


# In[9]:


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


# In[10]:


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


# In[11]:


# Number of iterations
res.num_iter


# In[12]:


# Optimal value function
res.v


# In[13]:


# Optimal policy
res.sigma


# In[14]:


# Transition probability matrix
res.mc.P


# In[15]:


# Simulate the controlled Markov chain
res.mc.state_values = S  # Set the state values
initial_state_value = 1
nyrs = 12
spath = res.mc.simulate(nyrs+1, init=initial_state_value)


# In[16]:


fig, axes = plt.subplots(1, 2, figsize=(12, 4))
axes[0].plot(np.arange(n)+1, res.v)
axes[0].set_xlim(1, 5)
axes[0].set_ylim(160, 220)
axes[0].set_xticks(np.linspace(1, 5, 5, endpoint=True))
axes[0].set_xlabel('Age of Machine')
axes[0].set_ylabel('Value')
axes[0].set_title('Optimal Value Function')

axes[1].plot(spath)
axes[1].set_xlim(0, nyrs)
axes[1].set_ylim(1, 4)
axes[1].set_yticks(np.linspace(1, 4, 4, endpoint=True))
axes[1].set_xlabel('Year')
axes[1].set_ylabel('Age of Machine')
axes[1].set_title('Optimal State Path')

plt.show()


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