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Periodicity and ruin probabilities for compound non-homogeneous poisson processes

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Compound non-homogenous Poisson processes with periodic claim intensity rates are studied in this work. A risk process related to a short term periodic environment and the periodicity for its compound claim counting process are discussed. The ruin probabilities of compound non-homogenous Poisson processes with periodic intensity function are also discussed, in which the embedded discrete risk model and the average arrival rate risk model are presented and bounds for the ruin probability of the continuous-time risk model are derived. We introduce a more general Poisson process model with double periodicity. Here the periodic environment does not repeat the exact same pattern every year but varies the short term peak over a relatively long period, with different levels in each year. Illustrations of periodicity for short and long term Poisson models and numerical examples for ruin probabilities are also given.

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