Ruin probabilities for a correlated aggregate claims

In this paper we consider a risk model having two disjoint classes of insurance business. Correlation may exist among the two claim number processes. Claim occurrences of both classes relate to Poisson and Erlang processes. We derive general solutions to the ultimate survival (ruin) probabilities for some risk processes generated from the assumed model when the claim sizes are exponentially distributed. In particular we study the correlated case in which both classes of claims occur as a mixture of Poisson and Erlang processes. We also examine the asymptotic property of the ruin probability for this special risk process with general claim size distributions.

Keywords: Bivariate compound Poisson; Correlated aggregate claims; Erlang process; Renewal process; Ruin probability.