A Robust Portfolio Selection Problem based on a Confidence Interval with Investor's Subjectiviety

This paper considers a robust portfolio selection problem considering a confidence interval with subjectivity to the weight for the standard deviation. Since the proposed model is formulated as an ill-defined problem due to fuzziness and bi-object derived from maximizing both robustness and investor's satisfaction level to the total profit, it is hard to solve it directly. Therefore, introducing fuzzy goals for the bi-objective functions, the proposed model is transformed into the deterministic equivalent problem. Furthermore, in order to obtain the exact optimal portfolio analytically, the solution method is developed introducing a parameter and doing the equivalent transformations.