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Tail asymptotics of random sum and maximum of log-normal risks

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  • Hashorva, Enkelejd
  • Kortschak, Dominik

Abstract

In this paper we derive the asymptotic behaviour of the survival function of both random sum and random maximum of log-normal risks. As for the case of finite sum and maximum investigated in Asmussen and Rojas-Nandayapa (2008) also for the more general setup of random sums and random maximum the principle of a single big jump holds. We investigate both the log-normal sequences and some related dependence structures motivated by stationary Gaussian sequences.

Suggested Citation

  • Hashorva, Enkelejd & Kortschak, Dominik, 2014. "Tail asymptotics of random sum and maximum of log-normal risks," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 167-174.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:167-174
    DOI: 10.1016/j.spl.2014.01.018
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    References listed on IDEAS

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    1. Jiang, Tao & Gao, Qingwu & Wang, Yuebao, 2014. "Max-sum equivalence of conditionally dependent random variables," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 60-66.
    2. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
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    Cited by:

    1. Nadarajah, Saralees, 2016. "Asymptotic expansions for bivariate normal extremes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 124-133.
    2. Enkelejd Hashorva & Lanpeng Ji, 2014. "Random Shifting and Scaling of Insurance Risks," Risks, MDPI, vol. 2(3), pages 1-12, July.

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