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A Kesten-type bound for sums of randomly weighted subexponential random variables

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  • Chen, Yiqing

Abstract

Sums of randomly weighted subexponential random variables have become an important research topic, but most works on the topic consider randomly weighted sums of finitely many terms. To extend the study to the case of infinitely many terms, we establish a Kesten-type upper bound for the tail probabilities of sums of randomly weighted subexponential random variables. As an application, we derive a precise asymptotic formula for the tail probability of the aggregate present value of subexponential claims, where the present value factor is determined according to the zero-coupon bond price.

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  • Chen, Yiqing, 2020. "A Kesten-type bound for sums of randomly weighted subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303074
    DOI: 10.1016/j.spl.2019.108661
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    References listed on IDEAS

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    1. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2012. "Tail probability of randomly weighted sums of subexponential random variables under a dependence structure," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1727-1736.
    2. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
    3. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
    4. Chen, Yiqing & Ng, Kai W. & Xie, Xiangsheng, 2006. "On the maximum of randomly weighted sums with regularly varying tails," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 971-975, May.
    5. Zhu, Chun-hua & Gao, Qi-bing, 2008. "The uniform approximation of the tail probability of the randomly weighted sums of subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2552-2558, October.
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    Cited by:

    1. Thomas Hitchen & Saralees Nadarajah, 2024. "Exact Results for the Distribution of Randomly Weighted Sums," Mathematics, MDPI, vol. 12(1), pages 1-22, January.
    2. 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).
    3. 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.

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