Portfolio investment optimization is the process of selecting the best portfolio out of the set of all projects being considered. A high financial return is not the only concern since minimization of associated risk is as important. Its objective should be set to maximize the expected return and minimize the risk in the investment as most data need to be justified based on vagueness and future values. Thus, the portfolio investment optimization problem under a fuzzy environment is studied here by incorporating a classical mathematical optimization model with the fuzzy theory. It is solved with the fuzzy chance-constrained integer programming model by linear programming under predetermined conditions and limitations. This study also uses both the credibility index and credibilistic risk index for measuring the investment return and investment risk. A numerical example is illustrated to demonstrate the effectiveness and benefits of the proposed algorithm.

Portfolio selection and optimization deal with the selection of the most suitable projects in a portfolio. The expected goals can be achieved while considering the balance among selected projects, to ensure that all selected projects consume resources effectively. This study proposes and compares multi-objective portfolio investment optimization algorithms under uncertain conditions. The investment return (in terms of the fuzzy net present value of the portfolio) and investment risk (in terms of the credibilistic risk index) have simultaneously been considered. In addition, fuzzy chance-constrained programming is introduced as an optimization constraint to handle such uncertainty by specifying a desired confidence level of the decision makers. The outcome of this study can then help decision makers to decide what projects and when to invest. Decision makers can deal with a limited budget with logical relationships, and within their desired financial and risk requirements.