# Applications of Compound Poisson Processes

I'm reading the book Non-Life Insurance Mathematics, an introduction with Stochastic Processes by Thomas Mikosch and I'm interested in applications of the Cramer-Lundberg Process to concrete examples in insurance. I tried unsuccessfully to search such examples on the Internet.

Could someone suggest to me a paper or a book where I can find something?

Thanks!

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Non-Life Insurance Mathematics...what a funny title. It took some Googling to figure out what this meant. –  cardinal Sep 8 '11 at 20:47
Is it Non-(Life Insurance) Mathematics, or is it (Non-Life) Insurance Mathematics. The first would probably be pretty big. –  Graphth Sep 14 '12 at 16:23

## 1 Answer

It depends on what do you mean with concrete examples because the main example is just a motivation of the model: there are claims $Y$ which the insurance company pays to its clients. These payments occurs at arrival times of some counting process and have some distribution. When the underlying counting process is a Poisson process and claims are iid random variables (also independent from the counting process) then the amount of total claims is a compound Poisson process: $$S_t = \sum\limits_{i=1}^{N_t}Y_n.$$

The model is not perfect of course and there are many more advanced models (see e.g. survey Ruin models with investment income by J. Paulsen).

Also, the very same model is applied to queuing theory, may be also interesting to you.

So please specify, which examples do you want to read about. If you are interested in the case when such model was applied in the real company, this place seems be more useful for wait for the answer on such a question.

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