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Vector-valued Coherent Risk Measures

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  • Touzi, Nizar
  • Meddeb, Moncef
  • Jouini, Elyès
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    Abstract

    We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random portofolio to valued measure of Risk. Necessary and sufficient conditions of coherent aggregation are provided

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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/353.

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    Date of creation: Nov 2004
    Date of revision:
    Publication status: Published in Finance and Stochastics, 2004, Vol. 8, no. 4. pp. 531-552.Length: 21 pages
    Handle: RePEc:dau:papers:123456789/353

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    Related research

    Keywords: Risk Aggregation; Liquidity Risk; Risk Measures;

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    Cited by:
    1. Henry, Marc & Galichon, Alfred & Ekeland, Ivar, 2012. "Comonotonic Measures of Multivariate Risks," Economics Papers from University Paris Dauphine 123456789/2278, Paris Dauphine University.
    2. Ignacio Cascos, 2006. "The Expected Convex Hull Trimmed Regions Of A Sample," Statistics and Econometrics Working Papers ws066919, Universidad Carlos III, Departamento de Estadística y Econometría.
    3. Burren, Daniel, 2013. "Insurance demand and welfare-maximizing risk capital—Some hints for the regulator in the case of exponential preferences and exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 551-568.
    4. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    5. Andreas H. Hamel & Birgit Rudloff & Mihaela Yankova, 2012. "Set-valued average value at risk and its computation," Papers 1202.5702, arXiv.org, revised Jan 2013.
    6. \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.
    7. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    8. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
    9. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520, arXiv.org, revised Nov 2006.
    10. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    11. Wei, Linxiao & Hu, Yijun, 2014. "Coherent and convex risk measures for portfolios with applications," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 114-120.
    12. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    13. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
    14. Areski Cousin & Elena Di Bernardinoy, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
    15. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate Risks And Depth-Trimmed Regions," Statistics and Econometrics Working Papers ws063815, Universidad Carlos III, Departamento de Estadística y Econometría.
    16. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    17. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS

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