In this paper, we propose robust portfolio optimization models for reward–risk ratios utilizing Omega, semi‐mean absolute deviation ratio, and weighted stable tail adjusted return ratio (STARR). We address the uncertainty in returns on assets by varying them in symmetric bounded intervals. The proposed robust reward–risk ratios preserve linearity in the resulting models, and hence are tractable. However, the robust models involve a sizably voluminous number of constraints, especially when the number of assets and scenarios is large. We employ the cutting plane algorithm to solve the proposed models in a much reduced time efficiently. We evaluate the performance of the robust reward–risk ratio models on the listed stocks of FTSE 100, Nikkei 225, S&P 500, and S&P BSE 500. The robust portfolio optimization models are found to outperform their conventional counterpart models in terms of statistics measured by the standard deviation, value at risk (VaR), conditional value at risk (CVaR), Sharpe ratio, and STARR ratio.

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The paper introduces the worst-case portfolio optimization models within the robust optimization framework for maximizing return through either the mean or median metrics. The risk in the portfolio is quantified by Gini mean difference. We put forward the worst-case models under the mixed and interval+polyhedral uncertainty sets. The proposed models turn out to be linear and mixed integer linear programs under the mixed uncertainty set, and semidefinite program under interval+polyhedral uncertainty set. The performance comparison of the proposed models on the listed stocks of Euro Stoxx 50, Dow Jones Global Titans 50, S&P Asia 50, consistently exhibit advantage over their conventional non-robust counterpart models on various risk parameters including the standard deviation, worst return, value at risk, conditional value at risk and maximum drawdown of the portfolio.2010 Mathematics Subject Classification. Primary: 91G10, 91B30, 62G35; Secondary: 90C90, 90C05, 90C11.