A discrete-time risk model with Poisson ARCH claim-number process

Abstract

In this paper, we propose a discrete-time risk model with the claim number following an integer-valued autoregressive conditional heteroscedasticity (ARCH) process with Poisson deviates. In this model, the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the impact of the Poisson ARCH dependence structure on the ruin probability.