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Confidence Levels for CVaR Risk Measures and Minimax Limits

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  • Anderson, Edward
  • Xu, Huifu
  • Zhang, Dali

Abstract

Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and it's impact on optimal decision making when we wish to minimize the respective risk measures. We also investigate the difference between the optimal solutions to the two optimization problems with identical objective function but under constraints on the two risk measures. We discuss the benefits of a sample average approximation scheme for the CVaR constraints and investigate the convergence of the optimal solution obtained from this scheme as the sample size increases. We use some portfolio optimization problems to investigate teh performance of the CVaR approximation approach. Our numerical results demonstrate how reducing the confidence level can lead to a better overall performanc e.

Suggested Citation

  • Anderson, Edward & Xu, Huifu & Zhang, Dali, 2014. "Confidence Levels for CVaR Risk Measures and Minimax Limits," Working Papers 2014_01, University of Sydney Business School, Discipline of Business Analytics.
    • Handle: RePEc:syb:wpbsba:2123/9943
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    File URL: http://hdl.handle.net/2123/9943
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    Cited by:

    1. Arash Gourtani & Huifu Xu & David Pozo & Tri-Dung Nguyen, 2016. "Robust unit commitment with $$n-1$$ n - 1 security criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 373-408, June.
    2. Arash Gourtani & Tri-Dung Nguyen & Huifu Xu, 2020. "A distributionally robust optimization approach for two-stage facility location problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 141-172, June.
    3. Xiaojiao Tong & Hailin Sun & Xiao Luo & Quanguo Zheng, 2018. "Distributionally robust chance constrained optimization for economic dispatch in renewable energy integrated systems," Journal of Global Optimization, Springer, vol. 70(1), pages 131-158, January.

    More about this item

    Keywords

    CVaR approximation; robust optimization; minimax; semi-infinate programming; distributional robust optimization; sample average approximation;
    All these keywords.

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