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 Niño/La Niña years. The properties of the model are discussed in detail. 1 Department of Mathematics and Statistics, Concordia University, Canada. 2 Department of Business Administration, University Carlos III of Madrid, Spain * This research was funded by the Natural Sciences and Engineering Council of Canada (NSERC) operating grant OGP0036860. On Double Periodic Non–Homogeneous Poisson Processes José Garrido and Yi Lu Department of Mathematics and Statistics Concordia University, Canada Department of Business Administration University Carlos III of Madrid, Spain