3.5 Investment Strategies 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% per year. You plan to withdraw $120,000 per year at the end of each year. A key performance measure is the stopping time T, the length of time until the fund is fully depleted. The system parameters are as follows: %% inputs BO= 500; %initial bond account SO= 500; %initial stock account mu= 0.08; %drift sigma= 0.12; %volatility Dt= 1; %year, time interval r=0.05; %risk free interest rate mT= 50; %maximum allowed years N=2000; %sample size There are two withdrawal strategies. (i) The first strategy is to withdraw $60,000 from the stock account and $60,000 from the bond account. If either account does not have $60,000, then the account will be emptied and the remaining amount withdrawn from the other account until both parts are depleted. (ii) Under the second strategy, other things being equal, we withdraw the money from the bond account until it is depleted, then withdraw the money from the stock account until it is empty. Q1: for strategy 1, simulate one run with 50 years. Plot the evolution of stock and bond accounts over time. Q2: for strategy 1, simulate N = 2000 runs. Find the mean, CI 95%, and histogram (distribution) of the stopping time T. Q3: for strategy 2, repeat the procedures in Q1 and Q2. Compare the distributions of the stopping time T under two strategies. Which strategy has longer stopping time