Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets
Abstract
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.
Related
- Continuous-Time Mean-Variance Portfolio Selection Reinforcement Learning Problems for a Markov Regime-Switching System with No-Shorting Constraints
- Optimal Transport for Continuous-Time Mean-Variance Portfolio Selection
- Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
- Constrained Mean Variance Portfolio Selection under Reflected Factor Dynamics: Stochastic Riccati Equations, Neumann Problems,and a Deep Solver
- Mean-Variance Portfolio Selection: Statistical Properties and Distributionally Robust Optimization
BibTeX
@misc{li2026dynamic,
title = {{Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets}},
author = {Xun Li and Yutian Wang and Xun Yu Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.16625},
eprint = {2607.16625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16625},
}
RIS
TY - UNPB
TI - Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets
AU - Xun Li
AU - Yutian Wang
AU - Xun Yu Zhou
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.16625
UR - https://arxiv.org/abs/2607.16625
AB - 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.
ER -