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Approximations of the tail probability of the product of dependent extremal random variables and applications

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  • Qu, Zhihui
  • Chen, Yu

Abstract

In this paper, we investigate the tail probability of the product X∏i=1nYi, where (X,Y1,…,Yn) follows a multivariate Sarmanov distribution. An explicit asymptotic formula is established for the tail probability of the product when X belongs to the Fréchet, Gumbel, or Weibull max-domain of attraction. As applications, we consider a discrete-time risk model with dependent insurance and financial risks, and obtain the asymptotic behavior for the (in)finite-time ruin probabilities.

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  • Qu, Zhihui & Chen, Yu, 2013. "Approximations of the tail probability of the product of dependent extremal random variables and applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 169-178.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:169-178
    DOI: 10.1016/j.insmatheco.2013.04.010
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    References listed on IDEAS

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    6. Tang, Qihe & Vernic, Raluca, 2007. "The impact on ruin probabilities of the association structure among financial risks," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1522-1525, August.
    7. 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.
    8. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
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    Cited by:

    1. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.

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