Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment |
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| Institution: | 1. School of Business Administration, Institute of Government Decision-making and Performance Evaluation, South China University of Technology, Guangzhou, 510640, China;2. School of Mathematics and Computer Science, Ningxia University, Yinchuan, Ningxia 750021, China;1. Glorious Sun School of Business and Management, DongHua University, Shanghai 200051, China;2. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;3. Antai College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052, China |
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| Abstract: | We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint. |
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