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New Robust Reward‐Risk Ratio Models with CVaR and Standard Deviation

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  • Lijun Xu
  • Yijia Zhou

Abstract

In this paper, we present two robust reward‐risk ratio optimization models. Two new models contain the worst case of not only conditional value‐at‐risk (CVaR), but also standard deviation (SD). Using properties of reward measure, CVaR measure, and standard deviation measure, new models can be proved to equivalent to min‐max problems. When the uncertainty set is an ellipsoid, new models can be further rewritten as second‐order cone problems step by step. Finally, we implement new models to portfolio problems. It shows that new models are robust and comparable with mean‐CVaR ratio model. Since considering standard deviation, allocation decision obtained by new models can give reasonable rewards according to personal preferences.

Suggested Citation

  • Lijun Xu & Yijia Zhou, 2022. "New Robust Reward‐Risk Ratio Models with CVaR and Standard Deviation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8304411
    DOI: 10.1155/2022/8304411
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    References listed on IDEAS

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    1. Liyan Xu & Bo Yu & Wei Liu, 2014. "The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    4. Liyan Xu & Bo Yu & Wei Liu, 2014. "The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, November.
    5. 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.
    6. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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