Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures

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Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures

TitleTail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures
Publication TypeJournal Article
Year of Publication2012
AuthorsHua, L, Joe, H
JournalInsurance Mathematics & Economics
Volume51
Pagination492-503
Date PublishedSEP
Type of ArticleArticle
ISSN0167-6687
KeywordsArchimedean copula, asymptotic full dependence, Copula, Elliptical distributions, Extreme value distributions, Regularly varying, Slowly varying
AbstractWe investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly varying tails, lead to a tail comonotonic dependence structure. For random variables that are in the maximum domain of attraction of either Frechet or Gumbel, we prove the asymptotic additivity property of Value at Risk and Conditional Tail Expectation. (C) 2012 Elsevier B.V. All rights reserved.
DOI10.1016/j.insmatheco.2012.07.006