Assume that Jungho's initial wealth is 100,000. The probability of loss distribution is given below and his utility function is U(W) = 2+3ln(W). Also assume that SG Insurance company has symmetric information on the probability of loss distribution.

loss amount probability 0 .80 20,000 .10 60,000 .05 90,000 .05

1) Find the pure premium and expected wealth. (4) 2) Find the expected utility without insurance. (3) 3) Assuming that Jungyae is under same situation and Jungyaes utility function of wealth is

U(W) = 10+root(W), Jungho and Jungyae have been offered full insurance at a cost of 16,000. Using risk premium, explain why they accept the insurance or not. (12) 4) Assuming that premium loading is 20% of pure premium, Jungho has been offered partial insurance with 2,000 deductible. Using expected utility, explain why Jungho accept the insurance or not. (8) 5) As risk is transferred from one party(insured) to another(insurer), incentives for behavior are changed. Explain major problems and how insurers can write contracts or come up with strategies. (6) PLEASE ANSWER (4), (5)