A portfolio selection model with borrowing constraint based on possibility theory

Authors:
Xue Deng;Rongjun Li
Affiliations:
Department of Mathematics, School of Science, South China University of Technology, Guangzhou, Guangdong 510640, China and School of Business Administration, South China University of Technology, ...;School of Business Administration, South China University of Technology, Guangzhou, Guangdong 510640, China
Venue:
Applied Soft Computing
Year:
2012

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Abstract

Compared with the conventional probabilistic mean-variance methodology, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. In this paper, the portfolio selection model with borrowing constraint is proposed by means of possibilistic mean, possibilistic variance, and possibilistic covariance under the assumption that the returns of assets are fuzzy numbers. And a quadratic programming model with inequality constraints is presented when the returns of assets are trapezoid fuzzy numbers. Furthermore, Lemke algorithm is utilized to solve the model. Finally, a numerical example of the portfolio selection problem is given to illustrate our proposed effective means and variances. The results of the numerical example also show that the investor can make different decisions according to different requirements for the values of expected returns. And the efficient portfolio frontier of the model with borrowing constraints can be easily obtained.