On Double Periodic Non-Homogeneous Poisson Processes

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact same short term pattern every year, but lets its peak intensity vary over a longer period. This model reflects periodic environments like those forming hurricanes, in alternating El Nino/La Nina year. The properties of the model are discussed in detail.