Continuous-Time Mean-Variance Portfolio Selection: A Reinforcement Learning Framework
39 Pages Posted: 29 May 2019
Date Written: May 5, 2019
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.
Keywords: Reinforcement learning, mean-variance portfolio selection, entropy regularization, stochastic control, value function, Gaussian distribution, policy improvement theorem
JEL Classification: C02, C61, C63, G11,
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