Question

7: Consider Emily who has a personal wealth of $10,000, and has a probability of 0.2 of losing her car worth $6,400 in an accident. Her utility (of wealth) function is given by  u(w) =  w^0.5, (w = wealth).     

(a) What is Emily's expected wealth, expected utility, and utility of expected wealth? How much would it cost her if she can insure "fully", and if this insurance is fair?

(b) For full insurance, what is the max amount Emily would pay? If she does not have any insurance, determine the certainty equivalent and the risk premium associated with her uncertain situation? Determine the difference if her utility of wealth function was instead  u(w) = 5w?

Answer 1

Part (A)

An actuarially fair premium would be one that exactly offset the expected value of the loss.

so an actuarially fair premium would be $1,280

Part (b)

certainity equivalent is the level of wealth that gives expected utility

maximum amount Emily would be willing to pay for the insurance

if utility function is

An actuarially fair premium would be one that exactly offset the expected value of the loss.

so an actuarially fair premium would be $1,280

certainity equivalent is the level of wealth that gives expected utility

maximum amount Emily would be willing to pay for the insurance