A company's cash position, measured in millions of dollars, follows a generalized Wiener process with a drift rate of 0.1 per month and a variance rate of 0.16 per month. The initial cash position is 2.0.
(a) What are the probability distributions of the cash position after 1 month, 6 months, and 1 year?
(b) What are the probabilities of a negative cash position at the end of 6 months and 1 year?
(c) At what time in the future is the probability of a negative cash position greatest?