Question

Consider an asset (say, a manufacturing plant) worth $70 million if sold in good shape. You are told that there is:

i. a 10% probability that the plant may sustain damages (“loss”) worth $10 million,

ii. a 6% probability of a $16 million loss,

iii. and a 2% probability of a $25 million loss.

a.) What is the actuarially fair value of insuring this plant?

b.)What would a plant owner with log utility be willing to pay for this insurance?

Answer 1

Actuarially fair value = .probability of loss*size of loss = .1*10+.06*16+.02*25 = 2.46 million

Willingness of the payer will depend upon the utility of the payer
Expected utility = .82*log(70)+.1*log(60)+.06*log(54)+.02*log(45) = 1.83
Utility after insurance = log(70-x), where x is the maximum willingness
log(X) = 1.83
X = 67.27
70-x = 67.27
x = 2.73 million