Multiperiod Mean-Variance Portfolio Optimization with General Correlated Returns

While rich empirical evidence always shows certain degree of dependency among different time periods for the returns of risky assets, the current literature on dynamic portfolio selection has been dominated by the results under an independency assumption, although in various forms. We consider in this paper a multiperiod mean-variance (MV) portfolio selection problem for a market with multiple risky assets whose returns are statistically correlated among time periods. Instead of assuming some particular stochastic processes to model the correlation, we adopt a formulation with a general form of correlation, which enables us to better matching our model with real markets. Recognizing the fact that, under this general setting, parameters in the portfolio policy become path-dependent adaptive processes themselves, we solve the problem analytically and derive an explicit form for the optimal portfolio policy, which remains as a linear affine function of the current wealth.