Asymptotics for sum-ruin probabilities of a bidimensional risk model with heavy-tailed claims and stochastic returns

Abstract

This paper considers a bidimensional risk model with geometric Lévy price processes and dependent heavy-tailed claims, where the two claim-number processes generated by the two different lines of business are almost arbitrarily dependent. When the distributions of the claims are subexponential with a positive lower Matuszewska index, an asymptotic formula for the finite-time sum-ruin probability is derived, which has a more transparent form when the distributions of the claims are regularly-varying-tailed and the two claim-number processes are homogeneous Poisson processes. Some simulation studies are conducted to verify the accuracy and sensitivity of the asymptotic result by employing the crude Monte Carlo method.