Time-consistent Strategy Multiperiod Mean Standard Deviation Portfolio Selection

The standard deviation is used to measure portfolio risk. Considering the transaction costs, borrowing constraints, and threshold constraints, a multiperiod mean standard deviation portfolio selection with the Vasicek stochastic interest rate model and risk preference is proposed. Based on the game theory, the model is transformed into a time-consistent dynamic programming problem. A novel discrete approximate iteration method is designed to obtain the optimal time-consistent portfolio strategy. Finally, the impact of borrowing constraints, threshold constraints, and different risk preference coefficients on multi-period mean standard deviation optimal time-consistent strategy are analyzed in empirical analysis. It can be concluded that the terminal wealth of the portfolio is positive, positive, and negative with borrowing constraints, threshold constraints, and risk preference coefficients, respectively. The unit risk of the portfolio is negative, negative, and positive with borrowing constraints, threshold constraints, and risk preference coefficients, respectively.