Analytical Reduction Method for New Type-2 Fuzzy Chance-Constrained Portfolio Selection Model

Abstract

In the traditional portfolio selection problem, asset returns are modeled as fuzzy variables with fuzzy return. However, this approach is limited in its ability to capture uncertainty accurately and in analytical model solving. Here, we aim to develop a new fuzzy chance-constrained portfolio model with a type-2 fuzzy return variable using a credibility measure. In real practice, an effective portfolio model under a new, more complex environment is required to improve instinctive imprecision. Here, we propose a novel analytical reduction method to transform our proposed model into a linear programing model with linear constraints, and use a linear programing tool to obtain optimal portfolio strategies. We first reformulate the portfolio model with type-2 fuzzy returns using two types of chance criteria. Next, we provide a new analytical method to solve the proposed model. Then, we present a numerical example with 20 asset returns described by a triangular membership function and use comparison testing to illustrate the advantages of our proposed method. The numerical results show that the relationship between investor tolerance of portfolio risk and the values attained for the four objective functions is in line with our expectations regarding the risk-return trade-off, and the comparison test results indicate that our proposed reduction method performs better than three existing methods. Our method provides an effective practice model for reformulating type-2 fuzzy portfolio problems using an analytical reduction method. Although a large number of existing type-2 fuzzy portfolio problems cannot be solved by our analytical method, it represents a new tool to solve these kinds of problems.