An insurer issues a portfolio of 100 automobile insurance policies. Of these 100
ID: 3364365 • Letter: A
Question
An insurer issues a portfolio of 100 automobile insurance policies. Of these 100 policies, one-half have a deductible of 10 and the other half have deductible of 0. The insurance policy pays the amount of damage in excess of the deductible subject to a maximum of 125 per accident. Assume: The number of automobile accidents per year per policy has a Poisson distribution with mean O.03. Given that an accident occurs, the amount of vehicle damage has the following distribution: 1/3 1/3 1/3 z=30 z = 150 z= 200. Pr(X = z) = Compute the total amount of claims the insurer expects to pay in a single year. Solutions: 275.Explanation / Answer
The mean number of automobile accidents per year = 0.03
Total number of claims out of 100 insurance policies per year = 100 * 0.03 = 3
Probability of having a deductible of 10 = 1/2
Probability of having a deductible of 0 = 1/2
Probability of claim of x = 30 is (1/2) * (1/3) = (1/6)
Probability of claim of x = 20 (=30-10) is (1/2) * (1/3) = (1/6)
As, Claim amount after substracting dedcutible in damage amount of 150 and 200 is greater than 125, the claim amount will be 125 when the damagae amount is 150 or 200.
Probability of claim of x = 125 is (1/3) + (1/3) = 2/3
Expected amunt of claim per accident is,
(1/6) * 30 + (1/6) * 20 + (2/3) * 125 = 91.66667
Total amount of claim = Expected amunt of claim per accident * Total number of claims out of 100 insurance policies per year
= 91.66667 * 3 = 275
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