Exploratory Continuous-Time Dual-Standard Mean-Variance Portfolio Selection: A Reinforcement Learning Method

We investigate the feasibility problem of designing reinforcement learning (RL) algorithms for exploratory continuous-time dual-standard mean-variance (MV) portfolio selection problems. The problem is intended to provide theoretical support in the design of the corresponding RL algorithms. We give the corresponding policy improvement theorem (PIT) by which the policy can be improved for an initial policy. Then, we show that by appropriately selecting the initial policy and relying on the PIT, the algorithm can converge to the optimal policy after a finite number of iterations. Finally, we give a k-function that can be used for the design of RL algorithms for this problem.