This is a stochastic processes transition matrix and stationary distribution question.

Problem 2 Consider the following rating transition matrix of a rm (With states labelled AAA, AA, A, BB, B, C, D) over one year. 0.8 0.2 0.3 0.7 0.1 0.1 0.8 P_ 0.5 0.5 0.5 0.5 1 a) Supposing transitions are stationary. What is the transition probability over 6 months from state AAA to AA? From state A to AAA? b) Suppose the chain starts at the stationary distribution. What is the average time of going from state AAA to AAA? c) Suppose the chain starts at the stationary distribution. The rm makes a cash ow C(t)=$1 million at the end of year t if it is in state AA, and $2 million per year if it is in state AAA. The discount rate is oz = 95%. What is the value V of the perpetual cash ow oered by the rm? Suppose that all cash ows are disbursed at the end of the year. The value V of a perpetuity is given by