[2412.16175] Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study

Quantitative Finance > Portfolio Management arXiv:2412.16175 (q-fin) [Submitted on 8 Dec 2024 (v1), last revised 28 Mar 2026 (this version, v3)] Title:Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study Authors:Yilie Huang, Yanwei Jia, Xun Yu Zhou View a PDF of the paper titled Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study, by Yilie Huang and 2 other authors View PDF Abstract:We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL approach that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black--Scholes markets without factors, we further devise an algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of the Sharpe ratio. We then carry out an extensive empirical study implementing this algorithm to compare its performance and trading characteristics, evaluated under a host of common metrics, with a large number of widely employed portfolio allocation strategies on S\&P 500 constituents. The result...