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 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 Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm into four variants, and carry out an extensive empirical study to compare their performance, in terms of a host of common metrics, with a large number of widely used portfolio allocation strategies on S&P 500 constituents. The results demonstrate that the continuous-time RL strategies are consistently among the best especially in a volatile bear market, and decisively outperform the model-based continuous-time counterparts by significant margins.

Bio: Yilie Huang is a Postdoctoral Research Scientist in the Department of Industrial Engineering and Operations Research at Columbia University, supervised by Professor Xun Yu Zhou. His research lies at the intersection of reinforcement learning (RL), stochastic control, and financial engineering, with a focus on developing and analyzing continuous-time RL algorithms to optimize financial and control systems under uncertainty.

Huang earned his PhD in Industrial Engineering and Operations Research at Columbia University in 2024, where he was advised by Professor Xun Yu Zhou. He also holds an M.S. in Operations Research from Columbia University (2018) and a B.S. in Mathematics and Applied Mathematics from Zhejiang University (2017).

Meeting Recording: https://ucsb.zoom.us/rec/share/KMKZKP7FxfNADCtzuIsOU30vT-NEZIjocAa41EYujRxlF9sjjhPNJD5LHqHQx-su.IiAHzwE3CWEFUuye

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