Suppose you have initial wealth (W 0) of $120, and part of this wealth is invested in an asset that is worth $100. However, there is a 25% probability that this asset will be completely destroyed by a re, and a 75% probability that a re won't occur. Your utility function is U (W ) = ln W, and the price of an insurance policy which fully insures this asset against risk of loss is $40.

A. In dollar and percentage terms, what is the premium loading for a full coverage insurance policy which costs $40?

C. Suppose you make an \optimal" insurance purchase. What will be the expected value and standard deviation of your wealth?

D. Suppose you have a friend who is identical in all respects to you, except her utility is U(W)=-W^-1, What coinsurance rate maximizes her expected utility? Who is more risk averse { you or your friend?

E. Now suppose that you can fully insure this re risk for $25. What is your optimal level of coinsurance at this price? What is your friend's optimal level of coinsurance?