# What are some examples of Compound Poisson processes in insurance?

I'm writing the Bachelor thesis but I need some information. I need to find some practical examples and applications of the Compound Poisson Process in insurance. Does anyone have any good examples?

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I think it's worth to give a link to the same question on MSE: math.stackexchange.com/questions/62847/… – Ilya Sep 14 '11 at 14:19
@ user1379 : You should have a look at Kyprianou's Book " Introductory lectures on fluctuations of Lévy processes with applications". Regards – TheBridge Sep 14 '11 at 15:07
Any time an insurer wants to write some kind of option on some kind of underlying that exhibits jumps. So sometimes when people model the probability of default for corporations (could be used in a CDS contract) they might use this type of approach. – John Aug 16 '12 at 15:35

An insurer might model the filing of claims as a Poisson process, but the cumulative amount of the claims as a compound Poisson process.

As an example, suppose a company has issued a large large number of auto liability policies that are geographically dispersed and have identical limits and driver risk profiles. The incidence of claims being made by policy holders would approximate a Poisson process, but each claim would be for a varying dollar amounts (following some other distribution taking on values between zero and the policy limit).

The car insurance example fits the Poisson model because a single claim (or the lack of a claim) in a particular period doesn't indicate that another claim is more or less likely in the near future. A bad example would be flood insurance policies in a concentrated coastal area. That's because the claims are likely to come in waves, so a single claim is likely to be followed by others.

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"claims are likely to come in waves." Har. – Michael Stern May 23 '14 at 13:51

Even if this is maybe a bit off-topic as you ask for an example in the context of insurance I want to give you two different examples:

1. Credit risk: In the Credit Risk Plus model the number of credit defaults in a portfolio is modelled by a Poisson distribution. If you model the loss given default as an independent random sequence then the total loss is compound Poisson. See e.g. http://www.fam.tuwien.ac.at/~schmock/Stable_Panjer_Recursion.html
2. Operational risk: in the same vein as in credit risk. If you model the number of operational losses of a bank by a Poisson distribution and the size of losses as an independent sequence then again you have a compound Poisson model. See e.g. works of Pavel Shevchenko: Calculation of aggregate loss distributions or Implementing Loss Distribution Approach for Operational Risk.
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