Value at risk of loan portfolio with fuzzy return rates

This paper proposes the concept of the value at risk (VaR) of the loan portfolio with fuzzy return rates, and presents three kinds of forms of the definitions by possibility measure, necessity measure, and credibility measure. When all the return rates are special triangular fuzzy variables, the equations of the definitions can first be transformed into crisp equivalents, then be calculated by the dichotomy method. When the membership functions of return rates are complex, fuzzy simulation is designed to calculate the VaR. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.