Vector-type precise large deviations for a nonstandard multidimensional risk model with some arbitrary dependence structures

Abstract

Consider a nonstandard multidimensional risk model in which the claim sizes from all lines of businesses, sharing a common claim-arrival renewal process, constitute a sequence of independent and identically distributed nonnegative random vectors, the common inter-arrival times are assumed to be arbitrarily dependent and the dependence between claim size vectors and their waiting times are also allowed to be arbitrary. Moreover, the claim sizes from different lines of businesses are supposed to be extended negatively dependent. Under some mild conditions, this paper achieves some vector-type precise large deviation formulae for aggregate claims of such multidimensional risk model in the presence of dominatedly-varying claim sizes. The obtained results extend some existing ones in the literature.