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Maxima of Sums of Heavy-Tailed Random Variables

Author

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  • Ng, K.W.
  • Tang, Q.H.
  • Yang, H.

Abstract

In this paper, we investigate asymptotic properties of the tail probabilities of the maxima of partial sums of independent random variables. For some large classes of heavy-tailed distributions, we show that the tail probabilities of the maxima of the partial sums asymptotically equal to the sum of the tail probabilities of the individual random variables. Then we partially extend the result to the case of random sums. Applications to some commonly used risk processes are proposed. All heavy-tailed distributions involved in this paper are supposed on the whole real line.

Suggested Citation

  • Ng, K.W. & Tang, Q.H. & Yang, H., 2002. "Maxima of Sums of Heavy-Tailed Random Variables," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 43-55, May.
    • Handle: RePEc:cup:astinb:v:32:y:2002:i:01:p:43-55_01
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    Cited by:

    1. Shen, Xinmei & Lin, Zhengyan, 2008. "Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3222-3229, December.
    2. Jaap Geluk & Qihe Tang, 2009. "Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables," Journal of Theoretical Probability, Springer, vol. 22(4), pages 871-882, December.
    3. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2014. "Closure property and maximum of randomly weighted sums with heavy-tailed increments," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 162-170.
    4. Zhengyan Lin & Xinmei Shen, 2013. "Approximation of the Tail Probability of Dependent Random Sums Under Consistent Variation and Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 165-186, March.
    5. Wang, Dingcheng & Tang, Qihe, 2004. "Maxima of sums and random sums for negatively associated random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 287-295, July.
    6. 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.
    7. Zhang, Chenhua, 2014. "Uniform asymptotics for the tail probability of weighted sums with heavy tails," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 221-229.

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