Gradually tolerant constraint method for fuzzy portfolio based on possibility theory

In financial markets, some nonprobabilistic factors can be modeled as fuzzy numbers. Based on possibility theory and the assumption that the returns of assets are triangular fuzzy numbers, a bi-objective nonlinear portfolio selection model is proposed in this paper. This model aims to maximize the future expected return and minimize the future expected risk. Moreover, the obtained nonlinear bi-objective model is equivalent to the linear bi-objective minimizing programming model on the basis of possibilistic mean and possibilistic variance. Using the gradually tolerant constraint method proposed in this paper, we give a numerical example to illustrate the efficiency of the proposed model and method. The proposed method in this paper has improvements in two aspects. One is that our method offers several satisfactory solutions for the same model compared with the linear weighted method of Chang (2009), which offers only one satisfactory solution according to the investor's risk preference degree. The other is that the effective frontier of our method is more efficient than that of the method proposed by Markowitz (1987) and Zhang (2007).