A company's cash position, massured in millions of dollars, follows a generalized Wiener pros 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 potion 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? 12:14. Suppose that is the yield on a perpetual government bond that pays interest at the rate of $1 per ainum Assume that is expressed with continuous compounding, that interest is paid continuously on the bond, and that x follows the proces x=x-x)+ where

a, e, and are positive constants, and dr is a Wiener process. What is the process followed by the bood price? What is the expected instantaneous retum (including inter and capital gains) to the holder of the bond?