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Second Order Asymptotics of Aggregated Log-Elliptical Risk

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  • Dominik Kortschak

    (Université de Lyon
    Université Lyon 1)

  • Enkelejd Hashorva

    (University of Lausanne)

Abstract

In this paper we establish the error rate of first order asymptotic approximation for the tail probability of sums of log-elliptical risks. Our approach is motivated by extreme value theory which allows us to impose only some weak asymptotic conditions satisfied in particular by log-normal risks. Given the wide range of applications of the log-normal model in finance and insurance our result is of interest for both rare-event simulations and numerical calculations. We present numerical examples which illustrate that the second order approximation derived in this paper significantly improves over the first order approximation.

Suggested Citation

  • Dominik Kortschak & Enkelejd Hashorva, 2014. "Second Order Asymptotics of Aggregated Log-Elliptical Risk," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 969-985, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9356-5
    DOI: 10.1007/s11009-013-9356-5
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    2. Serguei Foss & Andrew Richards, 2010. "On Sums of Conditionally Independent Subexponential Random Variables," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 102-119, February.
    3. Søren Asmussen & José Blanchet & Sandeep Juneja & Leonardo Rojas-Nandayapa, 2011. "Efficient simulation of tail probabilities of sums of correlated lognormals," Annals of Operations Research, Springer, vol. 189(1), pages 5-23, September.
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    Cited by:

    1. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.
    2. Yang Yang & Xinzhi Wang & Shaoying Chen, 2022. "Second Order Asymptotics for Infinite-Time Ruin Probability in a Compound Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1221-1236, June.

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