A model for portfolio selection based on fuzzy decision-making theory

In this paper, we study portfolio selection in crisp and fuzzy cases, and we propose corresponding model and algorithm in both cases. In two models, the risk is taken as the sum of the absolute deviation of the risky assets instead of covariance, the transaction cost is taken as V-shaped function of the difference between the existing and new portfolio. An efficient way is given to transform an optimal problem with non-linear objective function or non-linear constraint into a linear problem, which alleviates the computational difficulty greatly. The investor's subjective impact is reflected in the model of the fuzzy decision-making environment. Comparison and analysis of the two models is given via a numerical example.