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

Shijie Wang, Cen Chen and Xuejun Wang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 18, 9075-9085

Abstract: In this article we obtain some novel results on pairwise quasi-asymptotically independent (pQAI) random variables. Concretely speaking, let X1, …, Xn be n real-valued pQAI random variables, and W1, …, Wn be another n non negative and arbitrarily dependent random variables, but independent of X1, …, Xn. Under some mild conditions, we prove that W1X1, …, WnXn are still pQAI as well. Our result is in a general setting whether the primary random variables X1, …, Xn 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.

Date: 2017
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DOI: 10.1080/03610926.2016.1202287

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