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Discrete-time risk models on time series for count random variables. (English) Zbl 1230.91071
Summary: We consider various specifications of the general discrete-time risk model in which a serial dependence structure is introduced between the claim numbers for each period. We consider risk models based on compound distributions assuming several examples of discrete variate time series as specific temporal dependence structures: Poisson MA(1) process, Poisson AR(1) process, Markov Bernoulli process and Markov regime-switching process. In these models, we derive expressions for a function that allow us to find the Lundberg coefficient. Specific cases for which an explicit expression can be found for the Lundberg coefficient are also presented. Numerical examples are provided to illustrate different topics discussed in the paper.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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