Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

Abstract

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥ 1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.