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Classical formulations of the portfolio optimization problem, such as mean-variance or Value-at-Risk (VaR) approaches, can result in a portfolio extremely sensitive to errors in the data, such as mean and covariance matrix of the returns. In this paper we propose a way to alleviate this problem in a tractable manner. We assume that the distribution of returns is partially known, in the sense that only bounds on the mean and covariance matrix are available. We define the worst-case Value-at-Riskdoi:10.1287/opre.51.4.543.16101 fatcat:vkxgphnx7vdfxcrip5yxyskkii