Some comments and clarifications about solutions for problem set 3

Whenever you submit a problem set in Finance 4335, I highly recommend that you compare your work with the solutions that I post on the course blog. In the case of problem set 3, students seemed to have the most difficulty with problem 1, part B, and also problem 2, parts B and C.

In a nutshell, in 1B, Ned is willing to pay the most for insuring risk, since after all, he is the only one of the three who is risk averse; Dusty is risk neutral, whereas Lucky is risk loving. Indeed, as I show in the solution for 1B, Ned is willing to pay up to $12.64 more than the actuarially fair value of .25(100), which implies an insurance price of $37.64. Since Dusty is risk neutral, he is indifferent between having certain wealth of $115 and uncertain wealth with an expected value of $115; the most Dusty is willing to pay for insurance is its actuarially fair value of .25(100) = $25. Since Lucky is risk loving, he will only insure risk if it is available for a $4.46 discount from its actuarially fair value of $25, which comes to $20.54.

Also, in problem 2A, since you’re risk averse, the Bernoulli principle tells us that risk averters are happy to pay actuarially fair prices (in this case, $180). Also, in problem 2B, a price of $250 is acceptable because U($750) = 6.71 > expected utility of no insurance = 6.45. Finally, in problem 2C, the maximum price for full coverage is equal to the sum of the actuarially fair price of $180 plus the risk premium (189.04), or $369.04. Note that this also corresponds to the difference between the initial wealth of $1,000 and the certainty equivalent of wealth of $630.96 under the self-insurance option.