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Compound compound Poisson risk model. (English) Zbl 1224.91078

Summary: The compound Poisson risk models are widely used in practice. In this paper, the counting process in the insurance risk model is a compound Poisson process. The model is called compound compound Poisson risk model. Some basic properties and the ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli risk model is discussed.

MSC:

91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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