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Distortion risk measure under parametric ambiguity

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  • Shao, Hui
  • Zhang, Zhe George

Abstract

This study develops closed-form solutions for distortion risk measures (DRM) in extreme cases by utilizing the first two moments and the symmetry of underlying distributions. The resultant extreme-case distributions, encompassing the worst- and best-case distributions, are identified by the envelopes of the distortion functions. The findings of this study extend previous research on worst-case risk measures such as worst-case VaR, worst-case CVaR, worst-case RVaR, and worst-case spectral risk measure, by presenting a unified framework. Furthermore, the compact solutions enhance tractability in optimization problems involving these risk measures, particularly when the true underlying distribution is unknown, and the first two moments are uncertain. The application of the extreme-case DRMs is illustrated with real data sets through numerical examples.

Suggested Citation

  • Shao, Hui & Zhang, Zhe George, 2023. "Distortion risk measure under parametric ambiguity," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1159-1172.
    • Handle: RePEc:eee:ejores:v:311:y:2023:i:3:p:1159-1172
    DOI: 10.1016/j.ejor.2023.05.025
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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Belles-Sampera, Jaume & Guillen, Montserrat & Santolino, Miguel, 2016. "What attitudes to risk underlie distortion risk measure choices?," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 101-109.
    3. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    4. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    5. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    6. Mario Brandtner, 2016. "“Spectral Risk Measures: Properties and Limitations”: Comment on Dowd, Cotter, and Sorwar," Journal of Financial Services Research, Springer;Western Finance Association, vol. 49(1), pages 121-131, February.
    7. Steve Zymler & Daniel Kuhn & Berç Rustem, 2013. "Worst-Case Value at Risk of Nonlinear Portfolios," Management Science, INFORMS, vol. 59(1), pages 172-188, July.
    8. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    9. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    10. Ioana Popescu, 2007. "Robust Mean-Covariance Solutions for Stochastic Optimization," Operations Research, INFORMS, vol. 55(1), pages 98-112, February.
    11. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    12. 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.
    13. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    14. 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.
    15. Dimitris Bertsimas & Xuan Vinh Doan & Karthik Natarajan & Chung-Piaw Teo, 2010. "Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 580-602, August.
    16. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    17. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
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