Moderate deviations for multidimensional aggregate claims with arbitrary dependence between claim sizes and waiting times

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 non negative components allowed to be dependent on each other, and the inter-arrival times form a sequence of p-extended negatively dependent random variables. By allowing arbitrary dependence between claim sizes and waiting times, we obtain the moderate deviations for the multidimensional aggregate claims with consistently varying tails.