Journal
MATHEMATICAL FINANCE
Volume 30, Issue 4, Pages 1273-1308Publisher
WILEY
DOI: 10.1111/mafi.12281
Keywords
empirical study; entropy regularization; Gaussian distribution; mean-variance portfolio selection; policy improvement; reinforcement learning; simulation; stochastic control; theorem; value function
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Funding
- Nie Center for Intelligent Asset Management at Columbia
- Columbia University
- Nie Center for Intelligent Asset Management
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We approach the continuous-time mean-variance portfolio selection with reinforcement learning (RL). The problem is to achieve the best trade-off 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 prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm and its variant outperform both traditional and deep neural network based algorithms in our simulation and empirical studies.
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