Precise large deviations for aggregate claims in a multidimensional risk model with arbitrarily dependent claims and accident-arriving times

Consider a multidimensional risk model, in which an insurer is exposed to more than one type of claims sharing a common accident-number process, and each type of the individual claims and the accident inter-arrival times are, respectively, extended negatively dependent and identically distributed nonnegative random variables. In various insurance contexts, it is hard to assume some specific dependence between the claims and the inter-arrival times due to their complex interplay, and hence arbitrary dependence is allowed in this paper. Under the assumption of the individual claims possessing dominatedly varying tails and some moment condition on the inter-arrival times, this paper establishes a precise large deviation result for the aggregate claim vector.