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

Authors

Guang Yang^{1, *}, Mei Cai^1, , Jindong Qin², Xinwang Liu³, Xu Zhang^1,

¹School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

²School of Management, Wuhan University of Technology, Wuhan, 430070, China

³School of Economics and Management, Southeast University, Nanjing, 211189, China

^*Corresponding author. Email: sanic2008azs@126.com

DOI

10.2991/ijcis.d.210507.001How to use a DOI?

Keywords

Type-2 fuzzy return; Analytical reduction method; Portfolio selection; Credibility measure

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.

Copyright

© 2021 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Guang Yang
AU  - Mei Cai
AU  - Jindong Qin
AU  - Xinwang Liu
AU  - Xu Zhang
PY  - 2021
DA  - 2021/05/26
TI  - Analytical Reduction Method for New Type-2 Fuzzy Chance-Constrained Portfolio Selection Model
JO  - International Journal of Computational Intelligence Systems
SP  - 1617
EP  - 1632
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210507.001
DO  - 10.2991/ijcis.d.210507.001
ID  - Yang2021
ER  -