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Asymptotic behavior of the empirical conditional value-at-risk

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  • Gao, Fuqing
  • Wang, Shaochen

Abstract

We study asymptotic behavior of the empirical conditional value-at-risk (CVaR). In particular, the Berry–Essen bound, the law of iterated logarithm, the moderate deviation principle and the large deviation principle for the empirical CVaR are obtained. We also give some numerical examples.

Suggested Citation

  • Gao, Fuqing & Wang, Shaochen, 2011. "Asymptotic behavior of the empirical conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 345-352.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:345-352
    DOI: 10.1016/j.insmatheco.2011.05.007
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    References listed on IDEAS

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    1. Takeda, Akiko & Kanamori, Takafumi, 2009. "A robust approach based on conditional value-at-risk measure to statistical learning problems," European Journal of Operational Research, Elsevier, vol. 198(1), pages 287-296, October.
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    5. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
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    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    9. Aharon Ben-Tal & Marc Teboulle, 2007. "An Old-New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476.
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    Cited by:

    1. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01491990, HAL.
    2. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Documents de travail du Centre d'Economie de la Sorbonne 17019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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