Advanced Search
MyIDEAS: Login to save this paper or follow this series

Vector-valued Coherent Risk Measures

Contents:

Author Info

  • Elyès Jouini

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

  • Moncef Meddeb

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Paris I - Panthéon-Sorbonne)

  • Nizar Touzi

    (CMAP - Centre de Mathématiques Appliquées - CNRS : UMR7641 - Université de Versailles Saint-Quentin-en-Yvelines (UVSQ) - Polytechnique - X)

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

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://halshs.archives-ouvertes.fr/docs/00/16/71/54/PDF/37-jmt.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00167154.

as in new window
Length:
Date of creation: 2004
Date of revision:
Publication status: Published, Finance and Stochastics, 2004, 8, 531-552
Handle: RePEc:hal:cesptp:halshs-00167154

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00167154
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: risk; measures;

Other versions of this item:

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

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. Imen Bentahar, 2006. "Tail Conditional Expectation for vector-valued Risks," SFB 649 Discussion Papers SFB649DP2006-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
  4. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
  5. Areski Cousin & Elena Di Bernardinoy, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
  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. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
  8. Davide La Torre & Marco Maggis, 2012. "A Goal Programming Model with Satisfaction Function for Risk Management and Optimal Portfolio Diversification," Papers 1201.1783, arXiv.org, revised Sep 2012.
  9. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520, arXiv.org, revised Nov 2006.
  10. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
  11. Wei, Linxiao & Hu, Yijun, 2014. "Coherent and convex risk measures for portfolios with applications," Statistics & Probability Letters, Elsevier, Elsevier, vol. 90(C), pages 114-120.
  12. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  13. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 119(C), pages 32-46.
  14. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
  15. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate Risks And Depth-Trimmed Regions," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws063815, Universidad Carlos III, Departamento de Estadística y Econometría.
  16. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, Elsevier, vol. 95(1), pages 20-40, January.
  17. 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.
  18. 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.
  19. 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.
  20. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
  21. Ignacio Cascos, 2006. "The Expected Convex Hull Trimmed Regions Of A Sample," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws066919, Universidad Carlos III, Departamento de Estadística y Econometría.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00167154. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.