Reinsurance Integration

[mcallist]

Hi,

This is a question from the flash cards with infinity in the limits of the integral. I'm always a little bit unsure about integrating when infinity is around and was wondering if someone could please explain it.

The solution in the flashcards uses integration by parts.

Here's the question.

Claim amounts have a Pareto distribution with parameters a = 3 and lambda = 120.
Calculate the mean claim amount paid by the reinsurer under excess of loss with retention limit 100.

Thanks in advance.
Tom

 

[John Lee]

Since claim sizes could be anything we model them with a distribution that has no upper limit.
However, we substituting in infinity everything will be fine as we will have terms of \(e^{-\infty}\) which tends to zero.

 

[mcallist]

Thanks a lot John.