Precise large deviations of aggregate claims in a size-dependent renewal risk model

Consider a renewal risk model in which claim sizes and inter-arrival 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-arrival time given the subsequent claim size being large. We study large deviations of the aggregate amount of claims. For a heavy-tailed case, we obtain a precise large-deviation formula, which agrees with existing ones in the literature.