# Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

arXiv: https://arxiv.org/abs/1802.04885 · HTML: https://mlsanity.com/paper/1802.04885/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 25 of 25)

- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty](https://mlsanity.com/paper/2404.12598/) (2024)
- [Mitigating Spurious Correlation via Distributionally Robust Learning with Hierarchical Ambiguity Sets](https://mlsanity.com/paper/2510.02818/) (2025)
- [On Generalization and Regularization via Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2212.05716/) (2022)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation](https://mlsanity.com/paper/2105.08037/) (2021)
- [Optimizer's Information Criterion: Dissecting and Correcting Bias in Data-Driven Optimization](https://mlsanity.com/paper/2306.10081/) (2023)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)
- [Choquet regularization for reinforcement learning](https://mlsanity.com/paper/2208.08497/) (2022)
- [Distributional Robustness Bounds Generalization Errors](https://mlsanity.com/paper/2212.09962/) (2022)
- [Wasserstein Distributionally Robust Regret Optimization](https://mlsanity.com/paper/2504.10796/) (2025)
- [Distributionally robust risk evaluation with a causality constraint and structural information](https://mlsanity.com/paper/2203.10571/) (2022)
- [Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning](https://mlsanity.com/paper/2303.15579/) (2023)
- [Nonlinear Distributionally Robust Optimization](https://mlsanity.com/paper/2306.03202/) (2023)
- [Sparse Portfolio Selection via Topological Data Analysis based Clustering](https://mlsanity.com/paper/2401.16920/) (2024)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [Adaptive Multi-task Learning for Multi-sector Portfolio Optimization](https://mlsanity.com/paper/2507.16433/) (2025)
- [Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization](https://mlsanity.com/paper/2509.22088/) (2025)
- [Generating Input Distributions for Explaining Portfolio Optimization Pipelines](https://mlsanity.com/paper/2606.25808/) (2026)
- [Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity](https://mlsanity.com/paper/2606.27610/) (2026)
- [Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization](https://mlsanity.com/paper/2607.09820/) (2026)
- [Optimal Transport Reweighting for Robust Learning under Spurious Correlations and Label Noise](https://mlsanity.com/paper/2610.01028/) (2026)

## Abstract (arXiv)

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the so-called Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend recent inference methodology in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way.