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Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

Part of: Multivariate analysis Applications

Published online by Cambridge University Press:  14 July 2016

Haijun Li  and
Yannan Sun
Haijun Li*
Affiliation:
Washington State University
Yannan Sun*
Affiliation:
Washington State University
*
∗Postal address: Department of Mathematics, Washington State University, Pullman, WA 99164, USA.
∗Postal address: Department of Mathematics, Washington State University, Pullman, WA 99164, USA.
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Abstract

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The tail dependence of multivariate distributions is frequently studied via the tool of copulas. In this paper we develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

Keywords

Tail dependenceheavy tailmultivariate regular variationcopulahazard rate orderingmultivariate elliptical distribution

MSC classification

Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 925 - 937
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Research supported in part by NSF grant CMMI 0825960.

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