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 costs on pro rata basis
b. A contract that pays $100 million in one-year’s time if losses exceed $200 million.