Portfolio selection based on fuzzy cross-entropy

In this paper, the Kapur cross-entropy minimization model for portfolio selection problem is discussed under fuzzy environment, which minimizes the divergence of the fuzzy investment return from a priori one. First, three mathematical models are proposed by defining divergence as cross-entropy, average return as expected value and risk as variance, semivariance and chance of bad outcome, respectively. In order to solve these models under fuzzy environment, a hybrid intelligent algorithm is designed by integrating numerical integration, fuzzy simulation and genetic algorithm. Finally, several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm.

[1]  Xiaotie Deng,et al.  A minimax portfolio selection strategy with equilibrium , 2005, Eur. J. Oper. Res..

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

[3]  Wei-Guo Zhang,et al.  On admissible efficient portfolio selection problem , 2004, Appl. Math. Comput..

[4]  K. V. Chow,et al.  ON VARIANCE AND LOWER PARTIAL MOMENT BETAS THE EQUIVALENCE OF SYSTEMATIC RISK MEASURES , 1994 .

[5]  Wen Lea Pearn,et al.  (Journal of Computational and Applied Mathematics,228(1):274-278)Optimization of the T Policy M/G/1 Queue with Server Breakdowns and General Startup Times , 2009 .

[6]  Xiang Li,et al.  A Sufficient and Necessary Condition for Credibility Measures , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[8]  Harry M. Markowitz,et al.  Computation of mean-semivariance efficient sets by the Critical Line Algorithm , 1993, Ann. Oper. Res..

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

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

[11]  Reuven Y. Rubinstein,et al.  Semi-Iterative Minimum Cross-Entropy Algorithms for Rare-Events, Counting, Combinatorial and Integer Programming , 2008 .

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

[13]  Amelia Bilbao-Terol,et al.  A fuzzy goal programming approach to portfolio selection , 2001, Eur. J. Oper. Res..

[14]  Rahib Hidayat Abiyev,et al.  Fuzzy portfolio selection using genetic algorithm , 2007, Soft Comput..

[15]  Brian M. Rom,et al.  Post-Modern Portfolio Theory Comes of Age , 1993 .

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

[17]  Chang-Chun Lin,et al.  Genetic algorithms for portfolio selection problems with minimum transaction lots , 2008, Eur. J. Oper. Res..

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

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

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

[21]  Enriqueta Vercher,et al.  Fuzzy portfolio optimization under downside risk measures , 2007, Fuzzy Sets Syst..

[22]  Виктор Павлович Маслов,et al.  О минимизации и максимизации энтропии в различных дисциплинах@@@On minimization and maximization of entropy in various disciplines , 2003 .

[23]  Baoding Liu,et al.  A note on chance constrained programming with fuzzy coefficients , 1998, Fuzzy Sets Syst..

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

[25]  Amelia Bilbao-Terol,et al.  Fuzzy compromise programming for portfolio selection , 2006, Appl. Math. Comput..

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

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

[28]  Yue Qi,et al.  Randomly generating portfolio-selection covariance matrices with specified distributional characteristics , 2007, Eur. J. Oper. Res..

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

[30]  S. Fang,et al.  Entropy Optimization and Mathematical Programming , 1997 .

[31]  Ghassem A. Homaifar,et al.  VARIANCE AND LOWER PARTIAL MOMENT BETAS AS ALTERNATIVE RISK MEASURES IN COST OF CAPITAL ESTIMATION: A DEFENSE OF THE CAPM BETA , 1990 .

[32]  An-Sing Chen,et al.  Using investment portfolio return to combine forecasts: A multiobjective approach , 2001, Eur. J. Oper. Res..

[33]  Zhimin Huang,et al.  Determination of the portfolio selection for a property-liability insurance company , 1996 .

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

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

[36]  Kin Keung Lai,et al.  A model for portfolio selection with order of expected returns , 2000, Comput. Oper. Res..

[37]  Yves Crama,et al.  Simulated annealing for complex portfolio selection problems , 2003, Eur. J. Oper. Res..

[38]  E. Elton.  Modern portfolio theory and investment analysis , 1981 .

[39]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[40]  Baoding Liu,et al.  Entropy of Credibility Distributions for Fuzzy Variables , 2008, IEEE Transactions on Fuzzy Systems.

[41]  James O. Williams.  Maximizing the Probability of Achieving Investment Goals , 1997 .

[42]  Pankaj Gupta,et al.  Asset portfolio optimization using fuzzy mathematical programming , 2008, Inf. Sci..

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

[44]  Maria Rosaria Simonelli.  Indeterminacy in portfolio selection , 2005, Eur. J. Oper. Res..