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Subexponentiality of the product of dependent random variables

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  • Yang, Haizhong
  • Sun, Suting

Abstract

Let X and Y be two nonnegative dependent random variables according to a copula function. Under appropriate conditions, the closure property of the product XY is derived when X belongs to class S and R, respectively. Some examples are provided to illustrate the impact of the dependence structure on the tail behavior of the product.

Suggested Citation

  • Yang, Haizhong & Sun, Suting, 2013. "Subexponentiality of the product of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2039-2044.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2039-2044
    DOI: 10.1016/j.spl.2013.05.017
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. Jiang, Jun & Tang, Qihe, 2011. "The product of two dependent random variables with regularly varying or rapidly varying tails," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 957-961, August.
    3. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    4. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
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    Cited by:

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    2. Li, Xiaohu & Wu, Jintang, 2014. "Asymptotic tail behavior of Poisson shot-noise processes with interdependence between shock and arrival time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 15-26.

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