A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios

•A fuzzy multi-objective higher order moment portfolio selection model is proposed.•A new entropy function based on Minkowski measure is proposed to obtain better diversification portfolios.•A new multi-objective evolutionary algorithm is designed to solve the proposed model efficiently.•Results show the effectiveness of the proposed portfolio mode.

Due to the important effect of the higher order moments to portfolio returns, the aim of this paper is to make use of the third and fourth moments for fuzzy multi-objective portfolio selection model. Firstly, in order to overcome the low diversity of the obtained solution set and lead to corner solutions for the conventional higher moment portfolio selection models, a new entropy function based on Minkowski measure is proposed as a new objective function and a novel fuzzy multi-objective weighted possibilistic higher order moment portfolio model is presented. Secondly, to solve the proposed model efficiently, a new multi-objective evolutionary algorithm is designed. Thirdly, several portfolio performance evaluation techniques are used to evaluate the performance of the portfolio models. Finally, some experiments are conducted by using the data of Shanghai Stock Exchange and the results indicate the efficiency and effectiveness of the proposed model and algorithm.