Continuous-Time Mean-Variance Portfolio Selection: A Reinforcement Learning Framework

Abstract

We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time-decaying variance. We then establish connections between the entropy-regularized MV and the classical MV, including the solvability equivalence and the convergence as exploration weighting parameter decays to zero. Finally, we prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm outperforms both an adaptive control based method and a deep neural networks based algorithm by a large margin in our simulations.

39 pages, 5 figures

References in corpus (6)

• Prioritized Experience Replay
• Benchmarking Deep Reinforcement Learning for Continuous Control
• A reinforcement learning extension to the Almgren-Chriss model for optimal trade execution
• Variance Adjusted Actor Critic Algorithms
• Exploration versus exploitation in reinforcement learning: a stochastic control approach
• Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

Cited by in corpus (1)

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