Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints

This paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control, in which the returns of assets are characterized by possibilistic mean values. A possibilistic absolute deviation is defined as the risk control of portfolio. A new multiperiod mean absolute deviation fuzzy portfolio selection model with transaction cost, borrowing constraints, threshold constraints and cardinality constraints is proposed. Based on the theory of possibility measure, the proposed model is transformed into a crisp nonlinear programming problem. Because of the transaction cost, the multiperiod portfolio selection is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy, and is proved convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.