Operator Tail Dependence of Copulas
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A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power scaling functions having possibly distinct tail indexes is investigated in detail. We show that the copulas with operator tail dependence, incorporated with regularly varying univariate margins, give rise to a rich class of the non-standard multivariate regularly varying distributions. We also show that under some mild conditions, the copula of a non-standard multivariate regularly varying distribution has the standard tail dependence of order 1. Some illustrative examples are given.
KeywordsOperator regular variation Tail dependence Extreme value analysis Tail risk
Mathematics Subject Classification (2010)62H20 62E20
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The author would like to sincerely thank referees and an associate editor for their insightful comments, which led to an improvement of the presentation and motivation of this paper. The author would also like to thank Mark Meerschaert for a useful discussion.
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