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PATHS AND INDICES OF MAXIMAL TAIL DEPENDENCE

Published online by Cambridge University Press:  19 June 2015

Edward Furman ,
Jianxi Su  and
Ričardas Zitikis
Edward Furman*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
Jianxi Su
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada E-Mail: [email protected]
Ričardas Zitikis
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize the notion to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are capable of differentiating between distinct risky positions in situations when the existing indices fail to do so.

Keywords

Multivariate distributioncopulatail dependencemaximal dependencefatal shockmultivariate Paretoenterprise risk management
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 3 , September 2015 , pp. 661 - 678
Copyright
Copyright © Astin Bulletin 2015 

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