# Large scale continuous-time mean-variance portfolio allocation via reinforcement learning

arXiv: https://arxiv.org/abs/1907.11718 · HTML: https://mlsanity.com/paper/1907.11718/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [The Evolution of Reinforcement Learning in Quantitative Finance: A Survey](https://mlsanity.com/paper/2408.10932/) (2024)
- [Robo-Advising: Enhancing Investment with Inverse Optimization and Deep Reinforcement Learning](https://mlsanity.com/paper/2105.09264/) (2021)
- [Discrete-Time Mean-Variance Strategy Based on Reinforcement Learning](https://mlsanity.com/paper/2312.15385/) (2023)
- [Improving Portfolio Optimization Results with Bandit Networks](https://mlsanity.com/paper/2410.04217/) (2024)

## Abstract (arXiv)

We propose to solve large scale Markowitz mean-variance (MV) portfolio allocation problem using reinforcement learning (RL). By adopting the recently developed continuous-time exploratory control framework, we formulate the exploratory MV problem in high dimensions. We further show the optimality of a multivariate Gaussian feedback policy, with time-decaying variance, in trading off exploration and exploitation. Based on a provable policy improvement theorem, we devise a scalable and data-efficient RL algorithm and conduct large scale empirical tests using data from the S&P 500 stocks. We found that our method consistently achieves over 10% annualized returns and it outperforms econometric methods and the deep RL method by large margins, for both long and medium terms of investment with monthly and daily trading.