On the analysis of a discrete-time risk model with INAR(1) processes

Abstract

This paper considers an extension of the classical discrete-time risk model for which an INAR(1) process is utilized to model a temporal dependence between the number of claims. We apply a recursive method for deriving the Laplace transform of the aggregate claims with or without discounting in this framework. This methodology is implemented for the class of INAR(1) processes with an arbitrary innovations' distribution. Three risk models via specific INAR(1) processes are studied when the distribution of the individual claim sizes belongs to the class of mixed Erlang distributions. These different models allow us to discuss the frequent manifestations of equidispersion, overdispersion and zero inflation, and to evaluate the distribution of the (discounted) aggregate claims. Numerical examples are performed in order to illustrate the results obtained in this paper.