An insurance company’s losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume that the risks taken on by the insurance company are entirely non-systematic.) The one-year risk-free rate is 5% per annum with annual compounding. 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 a pro rata basis
(b) A contract that pays $100 million in one-year’s time if losses exceed $200 million.