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March 2011 Extremal behavior of Archimedean copulas
Martin Larsson, Johanna Nešlehová
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Adv. in Appl. Probab. 43(1): 195-216 (March 2011). DOI: 10.1239/aap/1300198519

Abstract

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an l1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

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Martin Larsson. Johanna Nešlehová. "Extremal behavior of Archimedean copulas." Adv. in Appl. Probab. 43 (1) 195 - 216, March 2011. https://doi.org/10.1239/aap/1300198519

Information

Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1213.62084
MathSciNet: MR2761154
Digital Object Identifier: 10.1239/aap/1300198519

Subjects:
Primary: 60G70
Secondary: 60F05 , 62E20

Keywords: Archimedean copula , domain of attraction , ell_1-norm symmetric distribution , extreme value copula , regular variation , simplex distribution , tail dependence , threshold copula , Williamson transform

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 1 • March 2011
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