Survey on Multi-period Mean–Variance Portfolio Selection Model

Due to the non-separability of the variance term, the dynamic mean–variance (MV) portfolio optimization problem is inherently difficult to solve by dynamic programming. Li and Ng (Math Finance 10(3):387–406, 2000) and Zhou and Li (Appl Math Optim 42(1):19–33, 2000) develop the pre-committed optimal policy for such a problem using the embedding method. Following this line of research, researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints, realistic market assumptions and various financial applications. As the principle of optimality no longer holds, the pre-committed policy suffers from the time-inconsistent issue, i.e., the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t. The time inconsistency of the dynamic MV model has become an important yet challenging research topic. This paper mainly focuses on the multi-period mean–variance (MMV) portfolio optimization problem, reviews the essential extensions and highlights the critical development of time-consistent policies.