b. What are the long-run, steady-state probabilities? In other words, what fraction of time should you expect to spend in each of the four states? (10 points)
c. In the long-run, what is the average amount of additional risk premium you should expect to pay each year? (5 points)
Now suppose that the insurance company changes its approach: Instead of charging an additional risk premium, the company simply cancels the policy of any customer who has had an accident in each of two consecutive years.
d. Define and complete a transition probability matrix to represent this new approach. (15 points)
Note: This is a problem of model formulation. There is more than one way to structure a model to represent this situation. Again, my experience suggests that I won’t be able to provide you with any helpful hints. I especially won’t be able to reply to questions about whether you are “on the right track.”
e. Assume that you have not had any accidents in the last two years. Under the new approach, how many more years should you expect to hold this insurance policy before the company cancels it? (15 points)