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Robust risk management

Author

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  • 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
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. 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.
    3. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    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. 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, July.
    6. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2009. "Constructing Risk Measures from Uncertainty Sets," Operations Research, INFORMS, vol. 57(5), pages 1129-1141, October.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    11. 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.
    12. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    13. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Damien Gatt & Charles Yousif & Maurizio Cellura & Francesco Guarino & Kenneth Scerri & Ilenia Tinnirello, 2024. "A Novel Approach to Determine Multi-Tiered Nearly Zero-Energy Performance Benchmarks Using Probabilistic Reference Buildings and Risk Analysis Approaches," Sustainability, MDPI, vol. 16(1), pages 1-33, January.
    8. 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.
    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)," Other publications TiSEM eeb9c898-6943-4199-b747-3, Tilburg University, School of Economics and Management.
    10. 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.
    11. 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.
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    14. 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.

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