mlsanityData to 14 Oct 2026

Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets

arXiv 2607.16625 ↗First posted 18 Jul 2026math.OCcited by 0

On the map: Deep reinforcement learning methods → Adversarial robustness and RL in finance

Abstract (arXiv)

We study continuous-time mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets from a reinforcement learning (RL) perspective. The problem is a constrained stochastic linear -- quadratic control problem for which the entropy-regularized exploratory formulation of Wang et al. (2020) leads to difficulty in theoretical analysis, because enforcing the constraint on the support of randomized policies nullifies the tractable Gaussian exploration. To tackle this challenge, we introduce an auxiliary exploratory problem without entropy in which exploratory policies are still Gaussian whose samples may violate the no-shorting requirement but their means satisfy it. We then prove that, for a suitable choice of exploration variance, the mean of the optimal Gaussian policy of the auxiliary problem coincides with the optimal policy of the original problem. Motivated by this theoretical result, we develop a model-free RL algorithm that learns the optimal policy of the auxiliary (and hence the original) problem directly from trajectory data without estimating the investment opportunity set. A numerical example demonstrates the performance of the proposed algorithm.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods. Builds on 10 of its 23 references that are in the map. First posted on arXiv 18 Jul 2026.

Builds on

10 of 23 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study8 Dec

Other references · 9

  1. 2021Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithmscited by 101
  2. 2022q-Learning in Continuous Timecited by 91
  3. 2021Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approachcited by 84
  4. 2021Exploratory HJB equations and their convergencecited by 32
  5. 2023Fast Policy Learning for Linear Quadratic Control with Entropy Regularizationcited by 13
  6. 2024Entropy annealing for policy mirror descent in continuous time and spacecited by 12
  7. 2022Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problemscited by 10
  8. 2023Data-Driven Merton's Strategies via Policy Randomizationcited by 8
  9. 2026Amortized Guidance for Image Inpainting with Pretrained Diffusion Modelscited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025Exploratory Mean-Variance with Jumps: An Equilibrium Approach
  2. 2026Exploratory Randomization for Discrete-Time Risk-Sensitive Benchmarked Investment Management with Reinforcement Learning
  3. 2025Exploratory Mean-Variance Portfolio Optimization with Regime-Switching Market Dynamics
  4. 2025Multi-period Asset-liability Management with Reinforcement Learning in a Regime-Switching Market
  5. 2025Data-Driven Long-Term Asset Allocation with Tsallis Entropy Regularization ↗
  6. 2024Reinforcement Learning for Jump-Diffusions, with Financial Applications
  7. 2026Reinforcement Learning for Risk-Sensitive Investment Management: a Free Energy--Entropy Duality Approach
  8. 2024Deep Reinforcement Learning and Mean-Variance Strategies for Responsible Portfolio Optimization