Abstract
In this paper, we consider the in nite-time absolute ruin probabilities in two types of time-dependent renewal risk models with a constant premium rate and a constant interest rate. In the two models, we both as- sume that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys some dependence structure. We derive an asymptotic formula and an upper bound for the in nite-time absolute ruin probabilities in the two dependent cases, respec- tively, with the claim-size distribution belonging to the intersection of the class J ( γ ), γ > 0, and the class R -∞.
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