A fund has a value of $1,000,000. Half of the fund is invested in a stock portfolio whose value follows the Geometric Brownian motion (geometric random walk model), and half is invested in bonds paying 5 percent per year. You plan to withdraw $120,000 per year at the end of each year. Your plan is to withdraw $60,000 from the stock portfolio and $60,000 from the bond portion. If either portion does not have $60,000, then the portion will be emptied and the remaining amount withdrawn from the other portion until both parts are depleted. Show the distribution of the length of time until the fund is fully depleted.

Now consider the following withdrawal policy. Other things being equal, we withdraw the money from the bond fund until it is depleted, then withdraw the money from the stock portfolio. Compare the distribution of the life of the funds with that obtained from the first strategy.

The system parameters are as follows:

%% inputs B0= 500; %initial bond fund S0= 500; %initial stock fund m= 0.08; %drift s= 0.12; %volatility dt= 1; %year, time interval r=0.05; %risk free interest rate mT= 50; %maximum allowed years N=2000; %sample size

Answer rating: 100% (QA)

Heres the Python code to simulate the scenarios and calculate the distributions python import numpy ... View the full answer