Portfolio selection with a new definition of risk

In the field of portfolio selection, variance, semivariance and probability of an adverse outcome are three best-known mathematical definitions of risk. Lots of models were built to minimize risk based on these definitions. This paper gives a new definition of risk for portfolio selection and proposes a new type of model based on this definition. In addition, a hybrid intelligent algorithm is employed to solve the optimization problem in general cases. One numerical example is also presented for the sake of illustration.

[1]  Philippe Jorion Value at risk: the new benchmark for controlling market risk , 1996 .

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

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

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

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

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

[7]  John R. Koza,et al.  Genetic Programming II , 1992 .

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

[9]  Xiaoxia Huang,et al.  Fuzzy chance-constrained portfolio selection , 2006, Appl. Math. Comput..

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

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

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

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

[14]  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 .

[15]  W. Ziemba,et al.  The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice , 1993 .

[16]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

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

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

[19]  Chi-Fu Huang,et al.  Foundations for financial economics , 1988 .

[20]  A. Roy Safety first and the holding of assetts , 1952 .

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

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

[23]  H. Konno,et al.  A FAST ALGORITHM FOR SOLVING LARGE SCALE MEAN-VARIANCE MODELS BY COMPACT FACTORIZATION OF COVARIANCE MATRICES , 1992 .

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

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

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

[27]  James C. T. Mao,et al.  Models of Capital Budgeting, E-V VS E-S , 1970, Journal of Financial and Quantitative Analysis.

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

[29]  W. Ziemba,et al.  Worldwide asset and liability modeling , 1998 .

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

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

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

[33]  Michael J. Siclari,et al.  The practice of Delta-Gamma VaR: Implementing the quadratic portfolio model , 2003, Eur. J. Oper. Res..