ASYMPTOTICS FOR RUIN PROBABILITIES IN LEVY-DRIVEN RISK MODELS WITH HEAVY-TAILED CLAIMS

Consider a bivariate Levy-driven risk model in which the loss process of an insurance company and the investment return process are two independent Levy processes. Under the assumptions that the loss process has a Levy measure of consistent variation and the return process fulfills a certain condition, we investigate the asymptotic behavior of the finite-time ruin probability. Further, we derive two asymptotic formulas for the finite-time and infinite-time ruin probabilities in a single Levy-driven risk model, in which the loss process is still a Levy process, whereas the investment return process reduces to a deterministic linear function. In such a special model, we relax the loss process with jumps whose common distribution is long tailed and of dominated variation.