On multivariate extensions of Value-at-Risk
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level set...
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| Veröffentlicht in: | Journal of multivariate analysis 2013-08, Vol.119, p.32-46 |
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| container_title | Journal of multivariate analysis |
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| creator | Cousin, Areski Di Bernardino, Elena |
| description | In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions. Several properties have been derived. In particular, we show that both these risk measures satisfy the positive homogeneity and the translation invariance property. Comparisons between univariate risk measures and components of multivariate VaR are provided. We also analyze how these measures are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Illustrations are given in the class of Archimedean copulas. |
| doi_str_mv | 10.1016/j.jmva.2013.03.016 |
| format | Article |
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Copulas and dependence Level sets of distribution functions Mathematical functions Multivariate analysis Multivariate probability integral transformation Multivariate risk measures Probability distribution Risk assessment Stochastic orders Studies |
| title | On multivariate extensions of Value-at-Risk |
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