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Set-valued average value at risk and its computation

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  • Andreas H. Hamel
  • Birgit Rudloff
  • Mihaela Yankova
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    Abstract

    New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both version over finite probability spaces. Several examples illustrate various features of the theoretical constructions.

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    File URL: http://arxiv.org/pdf/1202.5702
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1202.5702.

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    Date of creation: Feb 2012
    Date of revision: Jan 2013
    Publication status: Published in Mathematics and Financial Economics 7 (2), 229-246, (2013)
    Handle: RePEc:arx:papers:1202.5702

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    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    3. Touzi, Nizar & Meddeb, Moncef & Jouini, Elyès, 2004. "Vector-valued Coherent Risk Measures," Economics Papers from University Paris Dauphine 123456789/353, Paris Dauphine University.
    4. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    5. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    6. Elyès Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued Coherent Risk Measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167154, HAL.
    7. Henry, Marc & Galichon, Alfred & Ekeland, Ivar, 2012. "Comonotonic Measures of Multivariate Risks," Economics Papers from University Paris Dauphine 123456789/2278, Paris Dauphine University.
    8. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
    9. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 12, July.
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    Cited by:
    1. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2013. "Measuring risk with multiple eligible assets," Papers 1308.3331, arXiv.org, revised Mar 2014.
    2. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Oct 2013.
    3. \c{C}a\u{g}\in Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org.
    4. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, Springer, vol. 59(4), pages 811-836, August.

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