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

arXiv: https://arxiv.org/abs/2607.16625 · HTML: https://mlsanity.com/paper/2607.16625/

## 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.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 10 of 10)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [q-Learning in Continuous Time](https://mlsanity.com/paper/2207.00713/) (2022)
- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Exploratory HJB equations and their convergence](https://mlsanity.com/paper/2109.10269/) (2021)
- [Fast Policy Learning for Linear Quadratic Control with Entropy Regularization](https://mlsanity.com/paper/2311.14168/) (2023)
- [Entropy annealing for policy mirror descent in continuous time and space](https://mlsanity.com/paper/2405.20250/) (2024)
- [Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problems](https://mlsanity.com/paper/2209.07059/) (2022)
- [Data-Driven Merton's Strategies via Policy Randomization](https://mlsanity.com/paper/2312.11797/) (2023)
- [Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study](https://mlsanity.com/paper/2412.16175/) (2024)
- [Amortized Guidance for Image Inpainting with Pretrained Diffusion Models](https://mlsanity.com/paper/2605.13010/) (2026)

## 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.