  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
leterature, we consider that there exist some inderdependence 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, and 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.
