Learning equilibrium mean‐variance strategy
研究了强化学习框架下的动态均值-方差投资组合优化问题，引入熵正则化器促进探索，学习均衡策略，提出算法并证明收敛性，适用于不完全市场。
Abstract We study a dynamic mean‐variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time–inconsistency involved in a mean‐variance criterion, we aim to learn an equilibrium policy. Under an incomplete market setting, we obtain a semi‐analytical, exploratory, equilibrium mean‐variance policy that turns out to follow a Gaussian distribution. We then focus on a Gaussian mean return model and propose a reinforcement learning algorithm to find the equilibrium policy. Thanks to a thoroughly designed policy iteration procedure in our algorithm, we prove the convergence of our algorithm under mild conditions, despite that dynamic programming principle and the usual policy improvement theorem failing to hold for an equilibrium policy. Numerical experiments are given to demonstrate our algorithm. The design and implementation of our reinforcement learning algorithm apply to a general market setup.