ASYMPTOTIC BOUNDS FOR PRECISE LARGE DEVIATIONS IN A COMPOUND RISK MODEL UNDER DEPENDENCE STRUCTURES

In the paper, we consider a compound risk model, where all the claim sizes satisfy a dependence structure, and the accident inter-arrival time and the claim-number of the subsequent accident satisfy another dependence structure described by a conditional tail probability of the inter-arrival time given the subsequent claim-number. We obtain the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims, with a feature that the asymptotic bounds hold uniformly for all x in an infinite t -interval.