Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.

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

[2]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[3]  Baoding Liu,et al.  Continuity theorems and chance distribution of random fuzzy variables , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[5]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Liu Yian-Kui,et al.  Random fuzzy programming with chance measures defined by fuzzy integrals , 2002 .

[7]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[8]  Hiroshi Konno,et al.  SOLVING LARGE SCALE MEAN-VARIANCE MODELS WITH DENSE NON-FACTORABLE COVARIANCE MATRICES , 2001 .

[9]  A. Yoshimoto.  THE MEAN-VARIANCE APPROACH TO PORTFOLIO OPTIMIZATION SUBJECT TO TRANSACTION COSTS , 1996 .

[10]  Baoding Liu.  A Survey of Entropy of Fuzzy Variables , 2007 .

[11]  R. Agarwal,et al.  Recent progress on stage-structured population dynamics , 2002 .

[12]  Huibert Kwakernaak,et al.  Fuzzy random variables--II. Algorithms and examples for the discrete case , 1979, Inf. Sci..

[13]  Baoding Liu,et al.  Random fuzzy dependent-chance programming and its hybrid intelligent algorithm , 2002, Inf. Sci..

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

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

[16]  Xiaotie Deng,et al.  A linear programming algorithm for optimal portfolio selection with transaction costs , 2000, Int. J. Syst. Sci..

[17]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[18]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[19]  Xiaoxia Huang.  Portfolio selection with fuzzy returns , 2007, J. Intell. Fuzzy Syst..

[20]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments. , 1960 .

[21]  H. Markowitz.  Portfolio Selection: Efficient Diversification of Investments , 1971 .

[22]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

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

[24]  Baoding Liu,et al.  Redundancy optimization problems with uncertainty of combining randomness and fuzziness , 2004, Eur. J. Oper. Res..

[25]  Xiaoxia Huang,et al.  Two new models for portfolio selection with stochastic returns taking fuzzy information , 2007, Eur. J. Oper. Res..

[26]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[27]  Wansheng Tang,et al.  Random fuzzy renewal process , 2006, Eur. J. Oper. Res..

[28]  David B. Fogel,et al.  Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (IEEE Press Series on Computational Intelligence) , 2006 .

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

[30]  Jin Peng,et al.  Three types of models for stochastic scheduling with fuzzy information , 2003 .

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

[32]  Baoding Liu,et al.  Some inequalities of random fuzzy variableswith application to moment convergence , 2005 .

[33]  W. Sharpe.  A Simplified Model for Portfolio Analysis , 1963 .

[34]  M. Arenas,et al.  A fuzzy goal programming approach to portfolio selection , 2001 .

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

[36]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[37]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..