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Toward a Copula Theory for Multivariate Regular Variation

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Copulae in Mathematical and Quantitative Finance

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 213))

Abstract

Multivariate regular variation describes the relative decay rates of joint tail probabilities of a random vector with respect to tail probabilities of a norm of this random vector, and it is often used in studying heavy-tail phenomena observed in data analysis in various fields, such as finance and insurance. Multivariate regular variation can be analyzed in terms of the intensity measure or spectral measure but can also be studied by using the copula approach. In this paper, the basic ingredients of a measure-theoretic copula theory for multivariate regular variation are presented, and the method is based on extraction of scale-invariant extremal dependence from the intensity measure by standardizing its margins. Various examples as well as the advantages and disadvantages of the copula approach are also discussed.

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Acknowledgments

The author would like to sincerely thank the reviewer for his/her detailed comments, which led to an improvement of the presentation of this paper and also for pointing out a few references related to this work. The author also likes to thank Professor Piotr Jaworski for the invitation to contribute to this Volume.

Furthermore, he acknowledges that his research is supported by NSF grants CMMI 0825960 and DMS 1007556.

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Authors and Affiliations

  1. Department of Mathematics, Washington State University, Pullman, WA, USA

    Haijun Li

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  1. Haijun Li
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Correspondence to Haijun Li .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. School of Economics and Management, Free University of Bozen-Bolzano, Piazza Università 1, Bozen, 39100, Italy

    Fabrizio Durante

  3. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

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Li, H. (2013). Toward a Copula Theory for Multivariate Regular Variation. In: Jaworski, P., Durante, F., Härdle, W. (eds) Copulae in Mathematical and Quantitative Finance. Lecture Notes in Statistics(), vol 213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35407-6_9

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