🤖 AI Summary
This paper addresses robust portfolio optimization under uncertainty in mean–covariance estimates. We propose a novel robust risk-measurement framework based on the Gelbrich distance—introduced for the first time in the mean–covariance space—to quantify parameter ambiguity while incorporating prior structural information about the underlying distribution. Theoretically, we prove that, under mainstream risk measures including Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), the resulting robust optimization problem is equivalent to a regularized Markowitz model with a closed-form penalty term. Our method integrates optimal transport theory, convex analysis, and robust optimization, ensuring both statistical robustness and computational efficiency. Compared with existing approaches, our framework unifies treatment across multiple risk measures, supports large-scale real-time optimization, and significantly enhances model generalizability and practical applicability.
📝 Abstract
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.
