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Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

arXiv 1802.04885 ↗First posted 13 Feb 2018stat.MEcited by 24

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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.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Feb 2018.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 3; 2024: 2; 2025: 6; 2026: 3.

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  1. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  2. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  3. 2021Robustifying Conditional Portfolio Decisions via Optimal Transportcited by 12
  4. 2025Mitigating Spurious Correlation via Distributionally Robust Learning with Hierarchical Ambiguity Setscited by 7
  5. 2022On Generalization and Regularization via Wasserstein Distributionally Robust Optimizationcited by 6
  6. 2024Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penaltycited by 5
  7. 2025DRO: A Python Library for Distributionally Robust Optimization in Machine Learningcited by 5
  8. 2023Optimizer's Information Criterion: Dissecting and Correcting Bias in Data-Driven Optimizationcited by 4
  9. 2021Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximationcited by 3
  10. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  11. 2022Markov Decision Processes under Model Uncertaintycited by 2
  12. 2022Choquet regularization for reinforcement learningcited by 2
12 more
  1. 2022Distributional Robustness Bounds Generalization Errorscited by 2
  2. 2025Wasserstein Distributionally Robust Regret Optimizationcited by 2
  3. 2022Distributionally robust risk evaluation with a causality constraint and structural informationcited by 1
  4. 2023Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learningcited by 1
  5. 2023Nonlinear Distributionally Robust Optimizationcited by 0
  6. 2024Sparse Portfolio Selection via Topological Data Analysis based Clusteringcited by 0
  7. 2025Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Controlcited by 0
  8. 2025Adaptive Multi-task Learning for Multi-sector Portfolio Optimizationcited by 0
  9. 2025Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimizationcited by 0
  10. 2026Generating Input Distributions for Explaining Portfolio Optimization Pipelinescited by 0
  11. 2026Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimizationcited by 0
  12. 2026Optimal Transport Reweighting for Robust Learning under Spurious Correlations and Label Noisecited by 0