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 1-year risk-free rate is 5%. Estimate the cost of the following:
(a) A contract that will pay in 1 year's time 60% of the insurance company's costs on a pro rata basis
(b) A contract that pays $100 million in 1 year's time if losses exceed $200 million.