Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model

Abstract

This paper deals with a size-dependent renewal risk model in which claim sizes and inter-occurrence times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure described via the conditional distribution of the inter-occurrence time given the subsequent claim size being large. The impact of this dependence structure on the tail behavior of aggregated claims is investigated and then a precise large deviation formula for the aggregate amount of sub-exponential claims is obtained.