An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem

• We combine Markowitz and DEA cross-efficiency model for portfolio selection.
• We model uncertainty by considering the asset returns as trapezoidal fuzzy numbers.
• We use the NSGA-II algorithm to solve the model.
• We apply the proposed model for 52 firms listed in stock exchange market of Iran.

In this paper, a novel multi objective model is proposed for portfolio selection. The proposed model incorporates the DEA cross-efficiency into Markowitz mean–variance model and considers return, risk and efficiency of the portfolio. Also, in order to take uncertainty in proposed model, the asset returns are considered as trapezoidal fuzzy numbers. Due to the computational complication of the proposed model, the second version of non-dominated sorting genetic algorithm (NSGA-II) is applied. To illustrate the performance of our model, the model is implemented for 52 firms listed in stock exchange market of Iran and the results are analyzed. The results show that the proposed model is suitable in compared with Markowitz and DEA models due to considering return, risk and efficiency, simultaneously.

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