24.13. An insurance company’s losses of a particular type are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million.

(Assume no difference between losses in a risk-neutral world and losses in the real world.)

The one-year risk-free rate is 5%. Estimate the cost of the following:

(a) A contract that will pay in one year’s time 60% of the insurance company’s losses on a pro rata basis

(b) A contract that pays $100 million in one year’s time if losses exceed $200 million.