On the evaluation of risk models with bivariate integer-valued time series

In this paper, we consider two bivariate risk models, which allow dependencies among the claim frequencies of an insurance portfolio. These models are described by the Poisson bivariate integer-valued moving-average process of order 1 (BINMA(1)) and the Poisson bivariate integer-valued autoregressive process of order 1 (BINAR(1)). For each proposed model, we derive an expression for the joint moment generating function of the bivariate aggregate claim amount. We present the distribution of the bivariate aggregate claim amount when the individual claim sizes are exponentially distributed. We provide numerical examples for computing related quantities such as the dependency measures, stop-loss premium, and tail risk measures.