# 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

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: $$S_t = \sum\limits_{i=1}^{N_t}Y_n.$$