Fuzzy portfolio model with different investor risk attitudes

We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.

[1]  S. Ramaswamy.  Portfolio Selection Using Fuzzy Decision Theory , 2005 .

[2]  Peijun Guo,et al.  Portfolio selection based on upper and lower exponential possibility distributions , 1999, Eur. J. Oper. Res..

[3]  W. Sharpe.  Portfolio Theory and Capital Markets , 1970 .

[4]  Kin Keung Lai,et al.  A class of linear interval programming problems and its application to portfolio selection , 2002, IEEE Trans. Fuzzy Syst..

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

[6]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[7]  Peijun Guo,et al.  Portfolio selection based on fuzzy probabilities and possibility distributions , 2000, Fuzzy Sets Syst..

[8]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[9]  André F. Perold,et al.  Large-Scale Portfolio Optimization , 1984 .

[10]  Valerio Lacagnina,et al.  A stochastic soft constraints fuzzy model for a portfolio selection problem , 2006, Fuzzy Sets Syst..

[11]  M. Best,et al.  The Efficient Set Mathematics When Mean-Variance Problems Are Subject to General Linear Constraints , 1990 .

[12]  Christer Carlsson,et al.  A Possibilistic Approach to Selecting Portfolios with Highest Utility Score , 2001, Fuzzy Sets Syst..

[13]  Jaroslava Hlouskova,et al.  The efficient frontier for bounded assets , 2000, Math. Methods Oper. Res..

[14]  Jun Li,et al.  A class of possibilistic portfolio selection model with interval coefficients and its application , 2007, Fuzzy Optim. Decis. Mak..

[15]  Xiang Li,et al.  A chance-constrained portfolio selection model with risk constraints , 2010, Appl. Math. Comput..

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

[17]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[18]  Alex W. H. Chan.  Merton, Robert C. , 2010 .

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

[20]  Lijian Chen,et al.  Mathematical programming models for revenue management under customer choice , 2010, Eur. J. Oper. Res..

[21]  Xiang Li,et al.  A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns , 2009, J. Comput. Appl. Math..

[22]  R. C. Merton,et al.  An Analytic Derivation of the Efficient Portfolio Frontier , 1972, Journal of Financial and Quantitative Analysis.

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

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

[25]  Wei-Guo Zhang.  Possibilistic mean-standard deviation models to portfolio selection for bounded assets , 2007, Appl. Math. Comput..

[26]  Jong-Shi Pang,et al.  A New and Efficient Algorithm for a Class of Portfolio Selection Problems , 1980, Oper. Res..

[27]  Wei-Guo Zhang,et al.  On admissible efficient portfolio selection policy , 2005, Appl. Math. Comput..

[28]  Xiaoxia Huang,et al.  Risk curve and fuzzy portfolio selection , 2008, Comput. Math. Appl..

[29]  J. Vörös,et al.  Portfolio analysis--an analytic derivation of the efficient portfolio frontier , 1986 .

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

[31]  Desheng Dash Wu,et al.  Portfolio selection using λ mean and hybrid entropy , 2011, Ann. Oper. Res..

[32]  Jiuping Xu,et al.  A novel portfolio selection model in a hybrid uncertain environment , 2009 .

[33]  Teresa León,et al.  Viability of infeasible portfolio selection problems: A fuzzy approach , 2002, Eur. J. Oper. Res..

[34]  Silvio Giove,et al.  An interval portfolio selection problem based on regret function , 2006, Eur. J. Oper. Res..

[35]  Wei Chen,et al.  On the possibilistic mean value and variance of multiplication of fuzzy numbers , 2009, J. Comput. Appl. Math..

[36]  Peter C. Fishburn,et al.  Retrospective on the utility theory of von Neumann and Morgenstern , 1989 .