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

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  • Lijun Xu
  • Yijia Zhou
  • Feng Feng

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.

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  • Lijun Xu & Yijia Zhou & Feng Feng, 2022. "New Robust Reward-Risk Ratio Models with CVaR and Standard Deviation," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, April.
    • Handle: RePEc:hin:jjmath:8304411
    DOI: 10.1155/2022/8304411
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    Cited by:

    1. Fang Xu & Mengfan Yan & Lun Wang & Shaojian Qu, 2022. "The Robust Emergency Medical Facilities Location-Allocation Models under Uncertain Environment: A Hybrid Approach," Sustainability, MDPI, vol. 15(1), pages 1-23, December.

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