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Approximation of the tail probability of randomly weighted sums and applications

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  • Zhang, Yi
  • Shen, Xinmei
  • Weng, Chengguo

Abstract

Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where {Xi,i>=1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and {[Theta]i,i>=1} is a sequence of nonnegative random variables, independent of {Xi,i>=1} and satisfying certain moment conditions. Under the assumption that {Xi,i>=1} has no bivariate upper tail dependence along with some other mild conditions, this paper establishes the following asymptotic relations: and as x-->[infinity]. In doing so, no assumption is made on the dependence structure of the sequence {[Theta]i,i>=1}.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:655-675
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    References listed on IDEAS

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    8. Yang, Yang & Jiang, Tao & Wang, Kaiyong & Yuen, Kam C., 2020. "Interplay of financial and insurance risks in dependent discrete-time risk models," Statistics & Probability Letters, Elsevier, vol. 162(C).
    9. 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.
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    14. Chen, Yiqing, 2020. "A Kesten-type bound for sums of randomly weighted subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 158(C).
    15. Lin, Jianxi, 2019. "Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 37-47.
    16. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
    17. Yang, Xiangfeng, 2015. "Exact upper tail probabilities of random series," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 13-19.
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