Joint tail of randomly weighted sums under generalized quasi asymptotic independence

Abstract: In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random variables, which is achieved by a combination of a new dependence structure with some two-dimensional heavy-tailed classes of distributions. Further, we introduce a new approach in two-dimensional regular varying distributions, that in contrast to well-established multivariate regularly varying distributions, is consistent with the multivariate non-linear single big jump principle. We study some closure properties of this, and of other two-dimensional classes. Our results contain the finite-time ruin probability in a two-dimensional discrete time risk model