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Asymptotic behavior of the empirical conditional value-at-risk

  • Gao, Fuqing
  • Wang, Shaochen
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711000655
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 3 ()
    Pages: 345-352

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:345-352
    DOI: 10.1016/j.insmatheco.2011.05.007
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. 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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    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    7. 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.
    8. 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.
    9. 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.
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