Multi-period Possibilistic Mean Semivariance Portfolio Selection with Cardinality Constraints and its Algorithm

In this paper, we consider a multi‐period portfolio selection problem in a fuzzy investment environment, in which the return and risk of assets are characterized by possibilistic mean value and possibilistic semivariance, respectively. Based on the theories of possibility, a new multi‐period possibislistic portfolio selection model is proposed, which contains risk control, transaction costs, borrowing constraints, threshold constraints and cardinality constraints. the proposed model can be transformed into a crisp nonlinear dynamic optimization problem by using fuzzy programming approach. Because of the transaction costs and cardinality constraints, the multi‐period portfolio selection is a mix integer dynamic optimization problem with path dependence A forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, a comparison analysis of the different cardinality constraints is provided to illustrate the efficiency of the proposed approaches and the designed algorithm.