Multi-period mean–semivariance portfolio optimization based on uncertain measure

In this paper, we discuss a multi-period portfolio selection problem when security returns are given by experts’ estimations. By considering the security returns as uncertain variables, we propose a multi-period mean–semivariance portfolio optimization model with real-world constraints, in which transaction costs, cardinality and bounding constraints are considered. Furthermore, we provide an equivalent deterministic form of mean–semivariance model under the assumption that the security returns are zigzag uncertain variables. After that, a modified imperialist competitive algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.