Portfolio selection problems considering fuzzy returns of future scenarios

This paper considers multi-criteria mathematical decision models with respect to portfolio selection problems, particularly multi-scenario models to the future return of each asset including ambiguity and the fuzzy extension of mean-variance model and mean-absolute deviation model. The proposed models are generally formulated as multi-criteria stochastic programming problems and fuzzy programming problems. Since they are not well-defined problems due to random and fuzzy variables and it is difficult to solve them directly and analytically, two cases with respect to proposed models are considered. Furthermore, introducing the possibility and necessity chance constraints, they are equivalently transformed into linear or quadratic programming problems and the efficient solution methods are constructed. Then, a numerical example of portfolio selection problem is given to compare proposal models with the basic model.