IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v222y2012i3p663-672.html
   My bibliography  Save this article

Robust risk management

Author

Listed:
  • Fertis, Apostolos
  • Baes, Michel
  • Lüthi, Hans-Jakob

Abstract

Estimating the probabilities by which different events might occur is usually a delicate task, subject to many sources of inaccuracies. Moreover, these probabilities can change over time, leading to a very difficult evaluation of the risk induced by any particular decision. Given a set of probability measures and a set of nominal risk measures, we define in this paper the concept of robust risk measure as the worst possible of our risks when each of our probability measures is likely to occur. We study how some properties of this new object can be related with those of our nominal risk measures, such as convexity or coherence. We introduce a robust version of the Conditional Value-at-Risk (CVaR) and of entropy-based risk measures. We show how to compute and optimize the Robust CVaR using convex duality methods and illustrate its behavior using data from the New York Stock Exchange and from the NASDAQ between 2005 and 2010.

Suggested Citation

  • Fertis, Apostolos & Baes, Michel & Lüthi, Hans-Jakob, 2012. "Robust risk management," European Journal of Operational Research, Elsevier, vol. 222(3), pages 663-672.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:663-672
    DOI: 10.1016/j.ejor.2012.03.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712002457
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    3. Zymler, Steve & Rustem, Berç & Kuhn, Daniel, 2011. "Robust portfolio optimization with derivative insurance guarantees," European Journal of Operational Research, Elsevier, vol. 210(2), pages 410-424, April.
    4. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    5. Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 1-33, May.
    6. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    2. Postek, K.S. & den Hertog, D. & Melenberg, B., 2014. "Tractable Counterparts of Distributionally Robust Constraints on Risk Measures," Other publications TiSEM c3a1df3e-f338-4989-806a-d, Tilburg University, School of Economics and Management.
    3. Postek, K.S. & den Hertog, D. & Melenberg, B., 2014. "Tractable Counterparts of Distributionally Robust Constraints on Risk Measures," Discussion Paper 2014-031, Tilburg University, Center for Economic Research.
    4. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    5. Barrieu, Pauline & Scandolo, Giacomo, 2014. "Assessing financial model risk," LSE Research Online Documents on Economics 60084, London School of Economics and Political Science, LSE Library.
    6. Aven, Terje, 2016. "Risk assessment and risk management: Review of recent advances on their foundation," European Journal of Operational Research, Elsevier, vol. 253(1), pages 1-13.
    7. Postek, K.S. & den Hertog, D. & Melenberg, B., 2015. "Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures (revision of CentER DP 2014-031)," Other publications TiSEM eeb9c898-6943-4199-b747-3, Tilburg University, School of Economics and Management.
    8. Mitra, Sovan & Karathanasopoulos, Andreas & Sermpinis, Georgios & Dunis, Christian & Hood, John, 2015. "Operational risk: Emerging markets, sectors and measurement," European Journal of Operational Research, Elsevier, vol. 241(1), pages 122-132.
    9. Postek, K.S. & den Hertog, D. & Melenberg, B., 2015. "Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures (revision of CentER DP 2014-031)," Discussion Paper 2015-047, Tilburg University, Center for Economic Research.
    10. Lagos, Guido & Espinoza, Daniel & Moreno, Eduardo & Vielma, Juan Pablo, 2015. "Restricted risk measures and robust optimization," European Journal of Operational Research, Elsevier, vol. 241(3), pages 771-782.
    11. Kellner, Ralf & Rösch, Daniel, 2016. "Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk," Journal of Economic Dynamics and Control, Elsevier, vol. 68(C), pages 45-63.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    2. Matmoura, Yassine & Penev, Spiridon, 2013. "Multistage optimization of option portfolio using higher order coherent risk measures," European Journal of Operational Research, Elsevier, vol. 227(1), pages 190-198.
    3. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    4. Ammann, Manuel & Coqueret, Guillaume & Schade, Jan-Philip, 2016. "Characteristics-based portfolio choice with leverage constraints," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 23-37.
    5. Allen, D.E. & McAleer, M.J. & Powell, R.J. & Singh, A.K., 2015. "Down-side Risk Metrics as Portfolio Diversification Strategies across the GFC," Econometric Institute Research Papers EI2015-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Hautsch, Nikolaus & Voigt, Stefan, 2019. "Large-scale portfolio allocation under transaction costs and model uncertainty," Journal of Econometrics, Elsevier, vol. 212(1), pages 221-240.
    7. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    8. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
    9. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2017. "Computational aspects of robust optimized certainty equivalents and option pricing," Papers 1706.10186, arXiv.org, revised Mar 2019.
    10. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    11. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    12. Aharon Ben-Tal & Dimitris Bertsimas & David B. Brown, 2010. "A Soft Robust Model for Optimization Under Ambiguity," Operations Research, INFORMS, vol. 58(4-part-2), pages 1220-1234, August.
    13. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised Aug 2020.
    14. R. I. Boţ & N. Lorenz & G. Wanka, 2010. "Dual Representations for Convex Risk Measures via Conjugate Duality," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 185-203, February.
    15. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    16. Carroll, Rachael & Conlon, Thomas & Cotter, John & Salvador, Enrique, 2017. "Asset allocation with correlation: A composite trade-off," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1164-1180.
    17. Hjalmarsson, Erik & Manchev, Petar, 2012. "Characteristic-based mean-variance portfolio choice," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1392-1401.
    18. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, University Library of Munich, Germany.
    19. Enrique Sentana, 2018. "Volatility, Diversification and Contagion," Working Papers wp2018_1803, CEMFI.
    20. Fulga, Cristinca, 2016. "Portfolio optimization with disutility-based risk measure," European Journal of Operational Research, Elsevier, vol. 251(2), pages 541-553.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:663-672. 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: (Haili He). General contact details of provider: http://www.elsevier.com/locate/eor .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.