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

TL;DR

This paper introduces a reinforcement learning framework for continuous-time mean-variance portfolio selection, deriving optimal Gaussian policies and demonstrating superior performance over existing methods through simulations.

Contribution

It formulates the MV problem as an entropy-regularized stochastic control, proves the Gaussian nature of optimal policies, and develops an RL algorithm with improved results.

Findings

Optimal policies are Gaussian with time-decaying variance.

The RL algorithm outperforms existing adaptive control and neural network methods.

Connections established between entropy-regularized and classical mean-variance problems.

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.