Some novel results on pairwise quasi-asymptotical independence with applications to risk theory

In this article we obtain some novel results on pairwise quasi-asymptotically independent (pQAI) random variables. Concretely speaking, let X₁, …, X_n be n real-valued pQAI random variables, and W₁, …, W_n be another n non negative and arbitrarily dependent random variables, but independent of X₁, …, X_n. Under some mild conditions, we prove that W₁X₁, …, W_nX_n are still pQAI as well. Our result is in a general setting whether the primary random variables X₁, …, X_n are heavy-tailed or not. Finally, a special case of above result is applied to risk theory for investigating the finite-time ruin probability for a discrete-time risk model with a wide type of dependence structure.