Periodicity and Ruin Probabilities for Compound Non - Homogeneous Poisson Processes

Periodicity and Ruin Probabilities for Compound Non-Homogenous Poisson Processes Compound non-homogenous Poisson processes with periodic claim intensity rates are stiidied 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 compo~md non-homogenous Poisson processes with periodic intensity function are also discussed, in which the embedded discrete risk model and the average carrival rate risk model are presented and bomds for the nùn probability of the continuous-time risk model are derived. We introduce a more general Poisson process mode1 with doiible 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 a r e n t levels in each year. Illustrations of periodicity for short and long term Poisson models and numerical examples for ruin probabilities are also given.