thesis_linear utility (multiplicative dynamic) 1b.py

# -*- coding: utf-8 -*-
"""
Created on Fri Apr 24 11:31:06 2020

@author: Lorenzo
"""
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import numpy as np
# import pandas as pd
from matplotlib import pyplot as plt
# from pylab import rcParams
# from collections import Counter
import matplotlib.pylab as pylab

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# storage vector for 20 trajectories
trajectories = np.zeros((20,10001))

# setting random seed
np.random.seed(6)

# stating wealth 100$ to feed the loop
w = 100

# loop that creates the trajectory
for i in range(0,20):
    w = 100
    for element in range(1,10001):
        if (w*1.01) - w > (0.5*(w*1.5) + 0.5*(w*0.6)) - w:
            w = w*1.01
            trajectories[i, element] = w
        else:
            if np.random.randint(0, 2, 1) == 1:
                w = w*1.5
                trajectories[i, element] = w
            else:
                w = w*0.6
                trajectories[i, element] = w
            
# 100$ at time t
trajectories[:,0] = 100

# defining expected utility factor
EU_factor = 1.05

# defining trajectory EU
trajectory_EU = list(100*(EU_factor)**(t) for t in range(0, 10001))

# plotting the trajectories
# plotting the trajectory
params = {'legend.fontsize': 'x-large',
          'figure.figsize': (15, 5),
         'axes.labelsize': 'x-large',
         'axes.titlesize':'x-large',
         'xtick.labelsize':'x-large',
         'ytick.labelsize':'x-large'}
pylab.rcParams.update(params)

plt.xlabel('time', fontdict=None, labelpad=None)
plt.ylabel('utility/wealth', fontdict=None, labelpad=None) 
plt.yscale('log')  
plt.grid()            
for i in range(0,20):
    plt.plot(trajectories[i,:])
plt.plot(trajectory_EU, color='red')

# saving the image
plt.savefig('thesis - linear utility 1b.pdf')

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