A mean-field formulation for optimal multi-period mean–variance portfolio selection with an uncertain exit time

A multi-period mean–variance portfolio selection problem with an uncertain exit time is one of the nonseparable dynamic optimization problems as the principle of optimality of dynamic programming no longer applies. In this paper, we introduce a mean-field formulation to tackle this multi-period nonseparable problem directly without introducing an embedding scheme. Moreover, we shed light on the efficient feature of the mean-field formulation when dealing with the issue of dynamic nonseparability.