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

ABSTRACT

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.

Keywords:

• Asymptotics
• consistent variation
• discrete-time risk model
• quasi-asymptotical independence
• ruin probability.

Acknowledgments

The authors would like to thank a referee for his/her insightful and constructive suggestions which have helped significantly improve the article.

Funding

This work was partially supported by the National Natural Science Foundation of China (11226207, 11201001), the Natural Science Foundation of Anhui Province (1508085J06), and the Provincial Natural Science Research Project of Anhui Colleges (KJ2017A024, KJ2017A028).