Mixed Poisson process with Pareto mixing variable and its risk applications∗

Abstract

This paper considers a mixed Poisson process with Pareto mixing variable, Exp-Pareto, and Erlang–Pareto distributions. New important properties of these distributions are derived.Approximations of the random time transformed Cramer–Lundberg collective risk model with Pareto mixing variable and different claim sizes, with finite or infinite means are given. The resulting risk model has dependent, Exp-Pareto interarrival times with Archimedean copulas.