Mean-covariance robust risk measurement

We introduce a universal framework for mean-covariance robust risk measurement andportfolio 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 andcomputational 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