Uncertain portfolio selection with high-order moments

In the mean-variance-skewness-kurtosis framework, this paper discusses an uncertain higher-order moment portfolio selection problem when security returns are given by experts’ evaluations. Based on uncertainty theory and the assumption that the security returns are zigzag uncertain variables, an uncertain multi-objective portfolio optimization model is proposed by considering the maximization of both the expected return and skewness of portfolio return while simultaneously minimizing the risk and kurtosis of portfolio return. Subsequently, the proposed model is transformed into a single-objective programming model by using fuzzy programming approach, in which investor preferences for high moments are incorporated. Furthermore, a modified flower pollination algorithm (MFPA) is developed for solution, in which PSO in local update strategy (PSOLUS) and dynamic switching probability strategy (DSPS) are employed to enhance the local searching and global searching abilities. Finally, a numerical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.