Tail Dependence from a Distributional Point of View |
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Authors: | Alessandro Juri Mario V Wüthrich |
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Institution: | (1) UBS AG, P.O. Box, CH-8098, Zurich;(2) Winterthur Insurance, Römerstrasse 17, P.O. Box 357, CH-8401 Winterthur |
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Abstract: | The dependence structure in the tails of bivariate random variables is studied by means of appropriate copulae. Weak convergence results show that these copulae are natural dependence structures for joint tail events. The results obtained apply to particular types of copulae such as archimedean copulae and the Gaussian copula. Further, connections to multivariate extreme value theory are investigated and a two-dimensional Pickands–Balkema–de Haan Theorem type is derived. Finally, a counterexample showing that the tail dependence coefficients do not completely determine the dependence structure of bivariate rare events is provided. |
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Keywords: | archimedean copula copula dependent risks extreme value theory regular variation tail dependence |
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