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On pairwise quasi-asymptotically independent random variables and their applications

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  • Li, Jinzhu

Abstract

In this paper we obtain some novel results regarding pairwise (strong) quasi-asymptotically independent random variables with dominatedly varying tails. Our main concern lies in the asymptotics for constant and randomly weighted sums of such random variables. The obtained results are applied to study the ultimate ruin probability of a claim-dependent risk model.

Suggested Citation

  • Li, Jinzhu, 2013. "On pairwise quasi-asymptotically independent random variables and their applications," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2081-2087.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2081-2087
    DOI: 10.1016/j.spl.2013.05.023
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    References listed on IDEAS

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    6. Chen, Yiqing & Ng, Kai W., 2007. "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 415-423, May.
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    Citations

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    Cited by:

    1. Yang, Haizhong & Li, Jinzhu, 2019. "On asymptotic finite-time ruin probability of a renewal risk model with subexponential main claims and delayed claims," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 153-159.
    2. 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.
    3. Yang Yang & Xinzhi Wang & Xiaonan Su & Aili Zhang, 2019. "Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim," Complexity, Hindawi, vol. 2019, pages 1-6, October.
    4. Liu, Yang & Chen, Zhenlong & Fu, Ke-Ang, 2021. "Asymptotics for a time-dependent renewal risk model with subexponential main claims and delayed claims," Statistics & Probability Letters, Elsevier, vol. 177(C).
    5. Hongmin Xiao & Lin Xie, 2018. "Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate," Risks, MDPI, vol. 6(4), pages 1-12, November.
    6. Dawei Lu & Meng Yuan, 2022. "Asymptotic Finite-Time Ruin Probabilities for a Bidimensional Delay-Claim Risk Model with Subexponential Claims," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2265-2286, December.
    7. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    8. 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).
    9. Jiang, Tao & Gao, Qingwu & Wang, Yuebao, 2014. "Max-sum equivalence of conditionally dependent random variables," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 60-66.
    10. Yuan, Meng & Lu, Dawei, 2023. "Asymptotics for a time-dependent by-claim model with dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 120-141.
    11. Zhang, Chenhua, 2014. "Uniform asymptotics for the tail probability of weighted sums with heavy tails," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 221-229.

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