عنوان مقاله [English]
This paper proposes a new model based on a Min-Max goal programming approach and using robust optimization model for the multi-objective portfolio selection problem. In Min-Max goal programming, decision-makers can achieve more than one
objective function. Some uncertain coefficients exist in both single and multi-objective models of the portfolio selection problem, which affect the feasibility and optimality of solutions. Robust optimization is an approach that deals with the uncertainty parameters in mathematical models and gu-arantees the feasibility of the solutions. This paper tries to address the uncertainty parameters with the robust optimization approach. This paper presents a Min-Max goal programming for the portfolio selection problem and addresses the uncertainty of the parameters by the use of robust optimization approach. For this purpose Markowitz Mean Variance model with two objectives, expected return and expected risk, has been transformed into a four-objective model under uncertainty by adding two new objectives, divided annual profit and stock price in the last day of exchange. Using this model, we may consider decision-makers' opinions and uncertainty together. At first, a min-max goal programming model is presented, and then to add uncertainty, the model is extended to a multi-objective robust model in which uncertainty exists in both
expected return and expected risk parameters. Bertsimas and Sim approach (2004) is utilized for robustness of our model. This robust model is linear and applied to optimize a sample of 20 stocks from Tehran Stock Exchange in a period of April 2013 to April 2014 under conditions of uncertainty. The results of the study show that the conservatism of the solution increases when the
price of robustness increases. So, the proposed model can efficiently confront uncertainty in multi-objective portfolio selection problem, and this model is more practical in the real world than others.