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Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums

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  • Xinmei Shen

    (Dalian University of Technology)

  • Kailin Du

    (Dalian University of Technology)

Abstract

The uniform approximation for the tail behavior of bidimensional randomly weighted sums is considered in this paper. The primary random vectors are supposed to have extended regularly varying tails, while the underlying dependence between the components is described by some quasi-extended-regular-variation (QERV) copula functions. There are mild moment conditions on the random weight vectors without any assumptions on the dependence structures between themselves. The case when the number of the sums is extended to an integer-valued random variable is investigated additionally. A direct application of the results in a stochastic difference equation and some numerical simulations are also stated.

Suggested Citation

  • Xinmei Shen & Kailin Du, 2023. "Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-25, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10000-x
    DOI: 10.1007/s11009-023-10000-x
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    References listed on IDEAS

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    1. Shen, Xinmei & Zhang, Yi, 2013. "Ruin probabilities of a two-dimensional risk model with dependent risks of heavy tail," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1787-1799.
    2. Qingwu Gao & Na Jin, 2015. "Randomly Weighted Sums of Pairwise Quasi Upper-Tail Independent Increments with Application to Risk Theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3885-3902, September.
    3. 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.
    4. Marc Goovaerts & Rob Kaas & Roger Laeven & Qihe Tang & Raluca Vernic, 2005. "The Tail Probability of Discounted Sums of Pareto-like Losses in Insurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2005(6), pages 446-461.
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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.

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