# Mean-Covariance Robust Risk Measurement

arXiv: https://arxiv.org/abs/2112.09959 · HTML: https://mlsanity.com/paper/2112.09959/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2021.

## Built on by (most cited first, 10 of 10)

- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Distributionally Robust Recourse Action](https://mlsanity.com/paper/2302.11211/) (2023)
- [Distributionally Robust Fair Principal Components via Geodesic Descents](https://mlsanity.com/paper/2202.03071/) (2022)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Distributionally Robust Causal Abstractions](https://mlsanity.com/paper/2510.04842/) (2025)
- [A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set](https://mlsanity.com/paper/2405.20124/) (2024)
- [Nonlinear Distributionally Robust Optimization](https://mlsanity.com/paper/2306.03202/) (2023)
- [Regularized Q-learning through Robust Averaging](https://mlsanity.com/paper/2405.02201/) (2024)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)
- [Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures](https://mlsanity.com/paper/2607.17018/) (2026)

## Abstract (arXiv)

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.