Portfolio selection with coherent Investor’s expectations under uncertainty

Abstract Fuzzy portfolio selection is effective in coping with the uncertainty in financial decision making, in which investor’s expectation plays an important role. In this paper, to capture the coherence of the investor’s expectation we develop a new trapezoidal fuzzy numbers with an adaptive index, through which the membership degrees for favorable and unfavorable scenarios are transformed consistently to avoid the logical confusion. We also present the possibilistic expected mean, variance and skewness under the new measurement. Then, the new trapezoidal fuzzy numbers are employed in fuzzy mean-variance model and mean-variance-skewness model for optimal asset allocation. The validity and advantages of these models can be illustrated by the numerical examples in the end.