Question

Steve, a private taxi driver, is considering having a car insurance. The probability that Steve causes a car accident is 0.05. With no car accident, Steve would earn $1,000. However, if Steve causes a car accident, he would earn only $500. With all the information given, answer the following questions a ~ d.

a. Calculate the expected income of Steve.

b. Let’s say that a car insurance premium is P and an insurance payment is C. Then, what is the condition for a car “fair” insurance for Steve? (Hint: Express as an equation using P, C, and Steve’ accident probability)

c. Assume that Steve is risk averse, and that the car insurance company would like to offer a fair insurance to him. Then, what would be the amount of the fair car insurance premium for Steve?

d. Assume that Steve became more risk averse after hearing that his friend taxi driver unfortunately got a car accident to death. Let’s say that the extent to which Steve is risk averse is doubled now. Then, with this doubled risk-aversion of Steve, what would be the amount of the fair car insurance premium for Steve?

Answer 1

a) . The probability that Steve causes a car accident is 0.05. With no car accident, Steve would earn $1,000. However, if Steve causes a car accident, he would earn only $500.

The expected income of Steve= 0.05*500+0.95*1000

25+950

=975

b)An insurance contract is actuarially fair if the premiums paid are equal to the expected value of the compensation received.

P = p ·A

where p is the expected probability of a claim, and C is the amount that the insurance company will pay in the event of an accident

c) A risk averse person will optimally buy full insurance if the insurance is actuarially fair. The insurance mount will cover the full loss.