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Asymptotics of Sum of Heavy-tailed Risks with Copulas

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Abstract

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each example we apply the main results to obtain the asymptotic expansions for Value-at-Risk of aggregate risk.

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Notes

  1. A compact set \(B\subset \left( 0,\infty \right) ^{2}\) is bounded away from 0.

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Acknowledgements

The authors gratefully acknowledge the anonymous referee and Editor for their helpful comments which resulted in a substantially improved version of this article. F. Yang gratefully acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (GrantNumber: 04242).

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Fan Yang

  2. Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    Yi Zhang

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  1. Fan Yang
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Correspondence to Fan Yang.

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Yang, F., Zhang, Y. Asymptotics of Sum of Heavy-tailed Risks with Copulas. Methodol Comput Appl Probab 25, 88 (2023). https://doi.org/10.1007/s11009-023-10066-7

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  • DOI: https://doi.org/10.1007/s11009-023-10066-7

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