An actuary is reviewing a study she performed on the size of claims she made ten

Question

An actuary is reviewing a study she performed on the size of claims she made ten years ago under homeowners insurance policies. In her study, she concluded that the size of claims followed an exponential distribution and the probability that a claim would be less than $1000 was 0.25. The actuary feels that the conclusions she reached in her study are still valid today with one exception: Every claim made today would be twice the size of a similar claim made ten years ago as a result of inflation.

Calculate the probability that the size of a claim made today is less than $1000.

Explanation / Answer

Determine the rate parameter from the equation F(1000) = 0.25,
Compute F(500) (note that 500 is the claim size corresponding to a claim size of 1000 today).

F(1000) = 1 ex = 0.25
1 e*1000 = 0.25
= 0.000287682

F(500) = 1 - e0.000287682*500=0.1340

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