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Multivariate value at risk and related topics

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  • András Prékopa

Abstract

Multivariate Value at Risk, or MVaR, is defined as the quantile set of a multivariate probability distribution. It has already been introduced and used in the literature under the name of p-Level Efficient Points, or pLEP’s, or briefly p-efficient points. Some of the topics connected with it are surveyed: discrete convexity, algorithmic generation, relation to logconcavity. A related notion: Multivariate Conditional Value at Risk, or MCVaR, is also introduced and some of its properties are explored. Finally, optimization problems, based on these notions, are presented and discussed, from the point of view of convexity and algorithmic solution. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • András Prékopa, 2012. "Multivariate value at risk and related topics," Annals of Operations Research, Springer, vol. 193(1), pages 49-69, March.
    • Handle: RePEc:spr:annopr:v:193:y:2012:i:1:p:49-69:10.1007/s10479-010-0790-2
    DOI: 10.1007/s10479-010-0790-2
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    References listed on IDEAS

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    1. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    2. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, October.
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    Cited by:

    1. Areski Cousin & Elena Di Bernardino, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
    2. Andre Luiz Diniz & Maria Elvira P. Maceira & Cesar Luis V. Vasconcellos & Debora Dias J. Penna, 2020. "A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning," Annals of Operations Research, Springer, vol. 292(2), pages 649-681, September.

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