Multiperiod mean-variance portfolio selection with intertemporal restrictions and correlated returns

This work studies the multiperiod mean-variance(MV) portfolio optimization problem with the intertemporal risk-reward restrictions and serially correlated returns. Motivated from the real investment practice, we generalize the existing multiperiod MV portfolio decision models by considering both the intermediate expected values and variances of the portfolio under a general market model with the serially correlated random returns. To conquer the non-separability of the variance terms in this model, we introduce an auxiliary problem which is in type of optimal Linear Quadratic(LQ) control model. Applying celebrated dynamic programming, we successfully derive the analytical optimal solution for such an auxiliary LQ control problem. Once we have such an analytical control policy, the optimal portfolio policy for original multiperiod MV portfolio selection model can be easily obtained. The revealed optimal portfolio policy is a linear affine function of the current wealth. Finally, we illustrate the solution scheme of our method through an example.