probability distribution for damage claims

Question

The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

Payment ($)Probability
0	0.81
500	0.08
1000	0.04
3000	0.03
5000	0.02
8000	0.01
10000	0.01

a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.

 

b. The insurance company charges an annual rate of  for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint:It is the expected payments from the company minus the cost of coverage.) Enter negative values as negative numbers.

 

Why does the policyholder purchase a collision policy with this expected value?

The policyholder is concerned that an accident will result in a big repair bill if there - Select your answer - (is no) (is) insurance coverage. So even though the policyholder has an expected annual loss of   , the insurance - Select your answer -(is not protecting) or (is protecting)against a large loss.

Answer 1

a. The expected value of the Benefit Premium for collision coverage is

(0 * 0.81) + (500 * 0.08) + (1000 * 0.04) + (3000 * 0.03) + (5000 * .02) + (8000 * 0.01) +(10000 * 0.01) = 450

Please note that an actual insurance company has other expenses (acquisition costs for the business, administrative expenses, taxes and employee compensation) and other income (investment income from reserves and surplus), so the Gross Premium charged to the policyholder for collision coverage will be different from the Benefit Premium for collisions.

b. The premium is not given as a numeric value. Assuming it to be P, the expected vale to the policyholder is 450 - P. So, if the collision Gross Premium is $600, the expected value to the policyholder is -$150.

The policyholder is concerned that an accident will result in a big repair bill if there is no insurance coverage. So even though the policyholder has an expected annual loss of $450 - P, the insurance is protecting against a large loss. This feature of normal human psychology is called risk aversion.