Abstract: A mean semi-absolute deviation model for multi-period portfolio selection in random environment is presented by taking into account transaction cost, borrowing constraints and diversification degree of portfolio. In the proposed model, the risk level is characterized by the semi-absolute deviation of return, and the diversification degree of portfolio is measured by the originally presented entropy. Because of the transaction costs, the multi-period portfolio selection is the dynamic optimization problem with path dependence. Furthermore, the discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the different entropy model is provided by a numerical example to illustrate that the entropy is more and the terminal wealth is less.

Key words: multi-period portfolio selection, mean semi-absolute deviation, entropy, transaction costs, discrete approximate iteration