Tail risk of multivariate regular variation

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Tail risk of multivariate regular variation

TitleTail risk of multivariate regular variation
Publication TypeJournal Article
Year of Publication2011
AuthorsJoe, H, Li, H
JournalMethodology and Computing in Applied Probability
Date PublishedDEC
Type of ArticleArticle
KeywordsCoherent risk, Copula, Regularly varying, Tail conditional expectation, Tail dependence
AbstractTail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.