Abstract: In this paper, a new multiperiod mean semi-absolute deviation portfolio selection model with total short sellingconstraints, threshold constraints, transaction costs and borrowing constraints is proposed. The return and the risk are quantified by the mean value of return and by the semi-absolute deviation of return, respectively. Because of the transaction costs, the proposed model is a dynamic optimization problem with path dependence. The proposed model is approximated to a dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy, and is proved linearly convergent.Finally, the comparison analysis of the different total short selling constraints and different preference coefficients in the portfolio is provided by numerical examples to illustrate the efficiency of the proposed method and the designed algorithm using real data from the Shanghai Stock Exchange.

Key words: multiperiod portfolio selection, mean semi-absolute deviation, total short selling constraints, V-shape transaction costs, the discrete iteration method