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?
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.
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:
- 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
- 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.