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

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.