Extreme dependence for multivariate data |
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Authors: | Damien Bosc Alfred Galichon |
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Affiliation: | 1. EDF R&2. D , 1 avenue du Général de Gaulle, Clamart , 92140 , France damien.bosc@polytechnique.edu;4. Sciences Po, Department of Economics , 28 rue des Saints-Pères, Paris , 75007 , France |
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Abstract: | This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the cross-covariance matrices, we also generalize the notion of positive upper dependence. We then propose a means to quantify the strength of the dependence between two given multivariate series and to increase this strength while preserving the marginal distributions. This allows for the design of stress-tests of the dependence between two sets of financial variables that can be useful in portfolio management or derivatives pricing. |
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Keywords: | Multivariate dependence Extreme dependence Covariance set |
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