Skewness of Fuzzy Numbers and Its Applications in Portfolio Selection

A fuzzy number is a normal and convex fuzzy subset of the real line. In this paper, based on membership function, we redefine the concepts of mean and variance for fuzzy numbers. Furthermore, we propose the concept of skewness and prove some desirable properties. A fuzzy mean-variance-skewness portfolio selection model is formulated and two variations are given, which are transformed to nonlinear optimization models with polynomial objective and constraint functions such that they can be solved analytically. Finally, we present some numerical examples to demonstrate the effectiveness of the proposed models.

[1]  The Geometric Portfolio Optimization with Semivariance in Financial Engineering , 2012 .

[2]  Henk Grootveld,et al.  Variance vs downside risk: Is there really that much difference? , 1999, Eur. J. Oper. Res..

[3]  Wei Yan,et al.  Multi-period semi-variance portfolio selection: Model and numerical solution , 2007, Appl. Math. Comput..

[4]  Xiaoxia Huang,et al.  Mean-Entropy Models for Fuzzy Portfolio Selection , 2008, IEEE Transactions on Fuzzy Systems.

[5]  Zhongfeng Qin,et al.  Portfolio selection based on fuzzy cross-entropy , 2009 .

[6]  Masahiro Inuiguchi,et al.  Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem , 2000, Fuzzy Sets Syst..

[7]  Xiaoxia Huang,et al.  Mean-semivariance models for fuzzy portfolio selection , 2008 .

[8]  Xiang Li,et al.  An expected regret minimization portfolio selection model , 2012, Eur. J. Oper. Res..

[9]  R. Huisman,et al.  Optimal Portfolio Selection in a Value-at-Risk Framework , 2001 .

[10]  Christer Carlsson,et al.  On Possibilistic Mean Value and Variance of Fuzzy Numbers , 1999, Fuzzy Sets Syst..

[11]  Wei-Guo Zhang,et al.  On Possibilistic Variance of Fuzzy Numbers , 2003, RSFDGrC.

[12]  Neil D. Pearson,et al.  Value at Risk , 2000 .

[13]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[14]  Minqing Xiao,et al.  Mean-Variance-Skewness-Kurtosis Portfolio Optimization with Return and Liquidity , 2012 .

[15]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[16]  E. Dotzauer,et al.  Optimal portfolios using linear programming models , 2004, J. Oper. Res. Soc..

[17]  Kin Keung Lai,et al.  Neural network-based mean-variance-skewness model for portfolio selection , 2008, Comput. Oper. Res..

[18]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[19]  Jonas Schmitt.  Portfolio Selection Efficient Diversification Of Investments , 2016 .

[20]  M. Inuiguchi,et al.  Mean-absolute-deviation-based fuzzy linear regression analysis by level sets automatic deduction from data , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[21]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[22]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[23]  Mohammad Modarres,et al.  Fuzzy turnover rate chance constraints portfolio model , 2013, Eur. J. Oper. Res..

[24]  Abraham Charnes,et al.  Chance Constrained Programming Approach to Empirical Analyses of Mutual Fund Investment Strategies , 1992 .

[25]  Xiang Li,et al.  Mean-variance-skewness model for portfolio selection with fuzzy returns , 2010, Eur. J. Oper. Res..

[26]  Susan X. Li.  An insurance and investment portfolio model using chance constrained programming , 1995 .

[27]  Masahiro Inuiguchi,et al.  Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints , 2013, Inf. Sci..

[28]  S. Liu,et al.  Mean-variance-skewness model for portfolio selection with transaction costs , 2003, Int. J. Syst. Sci..

[29]  Masahiro Inuiguchi,et al.  Portfolio selection under independent possibilistic information , 2000, Fuzzy Sets Syst..

[30]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[31]  Yusif Simaan.  Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model , 1997 .

[32]  Satoru Takahashi,et al.  Dynamic portfolio optimization with risk control for absolute deviation model , 2010, Eur. J. Oper. Res..

[33]  Umberto Cherubini,et al.  Fuzzy Value-at-risk: Accounting for Market Liquidity , 2001 .

[34]  Tsong-Yue Lai.  Portfolio selection with skewness: A multiple-objective approach , 1991 .