Mean--Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study
This work addresses portfolio optimization for investors in financial markets with unknown parameters, offering a practical and robust alternative to model-based methods, though it is incremental as it builds on existing reinforcement learning theory for diffusion processes.
The authors tackled continuous-time mean-variance portfolio selection in markets with unknown coefficients by developing a data-driven reinforcement learning algorithm that learns investment strategies directly, and demonstrated that the proposed strategy consistently performs among the best, decisively outperforming model-based counterparts by significant margins, especially in volatile bear markets.
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 algorithm 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 a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of the Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm and carry out an extensive empirical study to compare its performance, in terms of a host of common metrics, with a large number of widely employed portfolio allocation strategies on S\&P 500 constituents. The results demonstrate that the proposed continuous-time RL strategy is consistently among the best, especially in a volatile bear market, and decisively outperforms the model-based continuous-time counterparts by significant margins.