Question

1. Jill has $200,000 of valuables, faces a probability of .02 of burglary, in which she would lose jewelry worth $50,000. She can buy full insurance for $15,000 that would fully reimburse the $50,000 loss. Her utility function is u(x) = 2*sqrt(x) What is the actuarially fair price for the insurance policy? Should Jill buy this insurance policy? What is the most that Jill is willing to pay for an insurance policy that fully covers her against loss?

Answer 1

a) We know that at actuarially fair price of insurance expected losses on reimbursements get exactly equal to the price of the policy.

that is Fair price = Probability of loss * loss amount = 0.02*50,000 = $1000

the above is fair price and Jill has been charged with $15000 that is more than fair hence it is unfair full price of insurance.

b) In order to determine whether Jill should buy the policy, we have to compare her utility from being fully insured with the expected utility from being uninsured.

If she stays uninsured, she gets

Expected utility = 0.02*(2 sqrt(200,000 - 50,000))+ 0.98*(2 sqrt(200000)) = $33

If she gets insurance,

Expected utility = 2 sqrt(200,000 - 15000) = $860 approximately.

As her expected utility from buying insurance is more than not buying she should purchase the insurance.

c) She will pay until the EU from not buying gets equal to or lesser than EU from buying.

Thus, 33 = 2sqrt(200000 - M) Where M is the payment that she will pay most.

M = $199727

Thus Jill will pay $199727 maximum to buy insurance.

*From the given probability of 0.02 in the problem we get above results. Thank you.