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

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  • Shijie Wang
  • Cen Chen
  • Xuejun Wang

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.

Suggested Citation

  • Shijie Wang & Cen Chen & Xuejun Wang, 2017. "Some novel results on pairwise quasi-asymptotical independence with applications to risk theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9075-9085, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:18:p:9075-9085
    DOI: 10.1080/03610926.2016.1202287
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    Cited by:

    1. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.
    2. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Leipus, Remigijus & Paukštys, Saulius & Šiaulys, Jonas, 2021. "Tails of higher-order moments of sums with heavy-tailed increments and application to the Haezendonck–Goovaerts risk measure," Statistics & Probability Letters, Elsevier, vol. 170(C).

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