Bicriteria Exploratory Mean-Variance Portfolio Selection Problem in Continuous Time

This article studies a continuous-time mean-variance (MV) portfolio selection problem with reinforcement learning (RL). The MV problem is described by an exploratory, relaxed stochastic control problem, which is first proposed and developed by Wang et al. (2020) and Wang and Zhou (2020). Different from Wang and Zhou (2020), we minimize the variance and maximize the expected terminal return at the same time in the context of reinforcement learning, which is a generalization of Wang and Zhou (2020). By constructing an auxiliary problem, the optimal feedback control (or “policy” or “law”) for our problem is obtained, which is Gaussian with time-decaying variance.