Question:

a) Lucy who plans to retire in 18 years has decided to save money in the bank at the beginning of each month until her retirement, with each subsequent saving increase by 3%. During her retirement, she will withdraw $1000 at the beginning of each month of the following 15 years; with an increase of 5% for each withdrawal. Assuming a nominal yearly interest rate of 8% compounded continuously, how large should the initial saving be?

b) Consider a stock that pays no dividend on which a futures contract, a call option, and a put-option trade. The maturity date for all contracts is the same, the exercise price for both the put and the call is K, and the futures price is . Show that if K = F, then the call price equals the put price.

c) An investor with capital W can invest any amount between 0 and W, if V is invested then V is either won or lost, with respective probabilities q and 1-q. How much should be invested by an investor having a ln utility function if q=0.75? Sketch a graph of the investment against the probability q.