Mean-variance-skewness model for portfolio selection with fuzzy returns |
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Authors: | Xiang Li Zhongfeng Qin Samarjit Kar |
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Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;2. School of Economics and Management, Beihang University, Beijing 100191, China;3. Department of Mathematics, National Institute of Technology, Durgapur 713209, India |
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Abstract: | Numerous empirical studies show that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same. In order to measure the asymmetry of fuzzy portfolio return, a concept of skewness is defined as the third central moment in this paper, and its mathematical properties are studied. As an extension of the fuzzy mean-variance model, a mean-variance-skewness model is presented and the corresponding variations are also considered. In order to solve the proposed models, a genetic algorithm integrating fuzzy simulation is designed. Finally, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm. |
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Keywords: | Portfolio selection Fuzzy variable Mean-variance-skewness model Fuzzy programming Credibility measure |
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