RANDOM TIME RUIN PROBABILITY FOR THE RENEWAL RISK MODEL WITH HEAVY-TAILED CLAIMS

In this paper, we investigate the asymptotic behavior of the random time ruin probability for the renewal risk model with heavy-tailed claim sizes. Under the assumption that the claim sizes are independent and long-tailed, we give the equivalent conditions on asymptotic behavior for the random time ruin probability, where the independent or dependent structure among the inter-arrival times is not needed. While, under the assumption that the claim sizes are of some negative dependence structure and consistently varying tails, we obtain the sufficient condition of asymptotic behavior for the random time ruin probability which will require some negative dependence structure among the inter-arrival times.