Bellman type strategy for the continuous time mean-variance model

Abstract

To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that differs from the pre-committed and game-theoretic strategies. A comparison with the existing results on the continuous time mean-variance model shows that our method has several advantages. The explicit solutions of the dynamic optimal strategy and optimal wealth are given. When the dynamic optimal strategy is given at the initial time, we do not change it in the following investment time interval.