An interval mean–average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints

Interval number is a kind of special fuzzy number and the interval approach is a good method to deal with some uncertainty. An interval mean–average absolute deviation model for multiperiod portfolio selection is presented by taking risk control, transaction costs, borrowing constraints, threshold constraints and cardinality constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In the proposed model, the return and risk are characterized by the interval mean and interval average absolute deviation of return, respectively. Cardinality constraints limit the number of assets to be held in an efficient portfolio. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on interval theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. A forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the different desired number is provided by a numerical example to illustrate the efficiency of the proposed approach and the designed algorithm.