A review of credibilistic portfolio selection

Article

Abstract

This paper reviews the credibilistic portfolio selection approaches which deal with fuzzy portfolio selection problem based on credibility measure. The reason for choosing credibility measure is given. Several mathematical definitions of risk of an investment in the portfolio are introduced. Some credibilistic portfolio selection models are presented, including mean-risk model, mean-variance model, mean-semivariance model, credibility maximization model, α-return maximization model, entropy optimization model and game models. A hybrid intelligent algorithm for solving the optimization models is documented. In addition, as extensions of credibilistic portfolio selection approaches, the paper also gives a brief review of some hybrid portfolio selection models.

Keywords

Portfolio selection Credibility measure Fuzzy programming Risk curve 

References

  1. Arditti F.D. (1971) Another look at mutual fund performance. Journal of Financial and Quantitative Analysis 6: 909–912CrossRefGoogle Scholar
  2. Arenas-Parra M., Bilbao-Terol A., Rodríguez-Uría M.V. (2001) A fuzzy goal programming approach to portfolio selection. European Journal of Oprational Research 133: 287–297MATHCrossRefGoogle Scholar
  3. Bilbao-Terol A., Pérez-Gladish B., Arenas-Parra M., Rodríguez-Uría M.V. (2006) Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation 173: 251–264MATHCrossRefMathSciNetGoogle Scholar
  4. Bruckley J.J., Hayashi Y. (1994) Fuzzy genetic algorithm and applications. Fuzzy Sets and Systems 61: 129–136CrossRefMathSciNetGoogle Scholar
  5. Bruckley J.J., Feruing T. (2000) Evolution algorithm solution to fuzzy problems: Fuzzy linear programming. Fuzzy Sets and Systems 109: 35–53CrossRefMathSciNetGoogle Scholar
  6. Carlsson C., Fullér R., Majlender P. (2002) A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 131: 13–21MATHCrossRefMathSciNetGoogle Scholar
  7. Chunhachinda P., Dandapani K., Hamid S., Prakash A.J. (1997) Portfolio selection and skewness: Evidence from international stock market. Journal of Banking and Finance 21: 143–167CrossRefGoogle Scholar
  8. Colubi A., Fernández-García C., Gil M.A. (2002) Simulation of random fuzzy variables: An empirical approach to statistical/probabilistic studies with fuzzy experimental data. IEEE Transactions on Fuzzy Systems 10: 384–390CrossRefGoogle Scholar
  9. De Cooman G. (1997) Possibility theory I–III. International Journal of General Systems 25: 291–371MATHCrossRefMathSciNetGoogle Scholar
  10. Dubois D., Prade H. (1988) Possibility theory: An approach to computerized processing of uncertainty. Plenum, New YorkMATHGoogle Scholar
  11. Fama E. (1965) Portfolio analysis in a stable paretian market. Management Science 11: 404–419CrossRefGoogle Scholar
  12. Gupta P., Mehlawat M.K., Saxena A. (2008) Asset portfolio optimization using fuzzy mathe matical programming. Information Sciences 178: 1734–1755MATHCrossRefMathSciNetGoogle Scholar
  13. Holland J. (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann ArborGoogle Scholar
  14. Huang, X. (2004). Portfolio selection with fuzzy returns. Proceedings of the Second Annual conference on Uncertainty (pp. 21–29). Qinhuangdao July 16–20.Google Scholar
  15. Huang X. (2006) Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation 177: 500–507MATHCrossRefMathSciNetGoogle Scholar
  16. Huang X. (2007a) Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research 180: 396–405MATHCrossRefMathSciNetGoogle Scholar
  17. Huang X. (2007b) A new perspective for optimal portfolio selection with random fuzzy returns. Information Sciences 177: 5404–5414MATHCrossRefMathSciNetGoogle Scholar
  18. Huang X. (2007c) Portfolio selection with fuzzy returns. Journal of Intelligent & Fuzzy Systems 18: 383–390MATHGoogle Scholar
  19. Huang X. (2008a) Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics 217: 1–8MATHCrossRefMathSciNetGoogle Scholar
  20. Huang X. (2008b) Risk curve and fuzzy portfolio selection. Computers and Mathematics with Applications 55: 1102–1112MATHCrossRefMathSciNetGoogle Scholar
  21. Huang X. (2008c) Expected model for portfolio selection with random fuzzy returns. International Journal of General Systems 37: 319–328MATHCrossRefMathSciNetGoogle Scholar
  22. Huang X. (2008d) Portfolio selection with a new definition of risk. European Journal of Operational Research 186: 351–357MATHCrossRefMathSciNetGoogle Scholar
  23. Huang X. (2008e) Mean-entropy models for fuzzy portfolio selection. IEEE Transactions on Fuzzy Systems 16: 1096–1101CrossRefGoogle Scholar
  24. Huang, X. (2008f). Minimax mean-variance models for fuzzy portfolio selection, Technical Report.Google Scholar
  25. Huang, X. (2008g). Fuzzy minimax chance constrained models for portfolio selection, Technical Report.Google Scholar
  26. Huang, X. (2008h). Mean-variance model for hybrid portfolio selection with randomness and fuzziness, Technical Report.Google Scholar
  27. Ida M. (2002) Mean-variance portfolio optimization model with uncertain coefficients. Proceedings of IEEE International Conference on Fuzzy Systems 3: 1223–1226Google Scholar
  28. Inuiguchi M., Ramík J. (2000) Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems 111: 3–28MATHCrossRefMathSciNetGoogle Scholar
  29. Katagiri H., Ishii H. (1999) Fuzzy portfolio selection problem. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 3: III-973–III-978Google Scholar
  30. Kaufman A., Gupta M.M. (1985) Introduction to fuzzy arithmetic: Theory and applications. Van Nostrand Reinhold, New YorkGoogle Scholar
  31. Klir G.J., Yuan B. (1995) Fuzzy sets and fuzzy logic: Theory and applications. Prentice-Hall, New JerseyMATHGoogle Scholar
  32. Lacagnina V., Pecorella A. (2006) A stochastic soft constraints fuzzy model for a portfolio selection problem. Fuzzy Sets and Systems 157: 1317–1327MATHCrossRefMathSciNetGoogle Scholar
  33. León T., Liern V., Vercher E. (2002) Viability of infeasible portfolio selection problems: A fuzzy approach. European Journal of Operational Research 139: 178–189MATHCrossRefGoogle Scholar
  34. Li J., Xu J. (2009) A novel portfolio selection model in a hybrid uncertain environment. Omega 37: 439–449CrossRefGoogle Scholar
  35. Li P., Liu B. (2008) Entropy of credibility distributions for fuzzy variables. IEEE Transactions on Fuzzy Systems 16: 123–129CrossRefGoogle Scholar
  36. Li X., Liu B. (2007) Maximum entropy principle for fuzzy variable. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 15(Supp. 2): 43–52CrossRefGoogle Scholar
  37. Lin C.C., Liu Y.T. (2008) Genetic algorithm for portfolio selection problems with minimum transaction lots. European Journal of Operational Research 185: 393–404MATHCrossRefGoogle Scholar
  38. Liu B. (1998) Minimax chance constrained programming models for fuzzy decision systems. Information Sciences 112: 25–38MATHCrossRefMathSciNetGoogle Scholar
  39. Liu B. (2002) Theory and practice of uncertain programming. Physica-Verlag, HeidelbergMATHGoogle Scholar
  40. Liu B. (2004) Uncertainty theory: An introduction to its axiomatic foundations. Springer–Verlag, BerlinMATHGoogle Scholar
  41. Liu B. (2006a) A survey of credibility theory. Fuzzy Optimization and Decision Making 5: 387–408CrossRefMathSciNetGoogle Scholar
  42. Liu B. (2007) Uncertainty theory, 2nd edn. Springer–Verlag, BerlinMATHGoogle Scholar
  43. Liu B., Iwamura K. (1998) Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems 94: 227–237MATHCrossRefMathSciNetGoogle Scholar
  44. Liu B., Liu Y.K. (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10: 445–450CrossRefGoogle Scholar
  45. Liu Y.K. (2006b) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Transactions on Fuzzy Systems 14: 295–304CrossRefGoogle Scholar
  46. Markowitz H. (1952) Portfolio selection. Journal of Finance 7: 77–91CrossRefGoogle Scholar
  47. Markowitz H. (1959) Portfolio selection: efficient diversification of investments. Wiley, New YorkGoogle Scholar
  48. Nahmias S. (1978) Fuzzy variables. Fuzzy Sets and Systems 1: 97–110MATHCrossRefMathSciNetGoogle Scholar
  49. Oh K.J., Kim T.Y., Min S.H., Lee H.Y. (2006) Portfolio algorithm based on portfolio beta using genetic algorithm. Expert Systems with Applications-Intelligent Information Systems for Financial Engineering 30: 527–534Google Scholar
  50. Rahib H.A., Mustafa M. (2007) Fuzzy portfolio selection using genetic algorithm. Soft Computing—A Fusion of Foundations, Methodologies and Applications 11: 1157–1163MATHGoogle Scholar
  51. Rom B.M., Ferguson K.W. (1994) Post-modern portfolio theory comes of age. Journal of Investing 3: 11–17CrossRefGoogle Scholar
  52. Shoaf, J., & Foster, J. A. (1996). The efficient set GA for stock portfolios. Proceedings of the Decision Science Institute, Orlando (pp. 571–573).Google Scholar
  53. Simkowitz M., Beedles W. (1978) Diversification in a three moment world. Journal of Financial and Quantitative Analysis 13: 927–941CrossRefGoogle Scholar
  54. Skolpadungket, P., Dahal, K., & Harnpornchai, N. (2007). Portfolio optimization using multi-objective genetic algorithms. Proceeding of 2007 IEEE Congress on Evolutionary Computation (pp. 516–523).Google Scholar
  55. Tanaka H., Guo P. (1999) Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114: 115–126MATHCrossRefGoogle Scholar
  56. Tanaka H., Guo P., Türksen B. (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111: 387–397MATHCrossRefMathSciNetGoogle Scholar
  57. Tiryaki F., Ahlatcioglu M. (2005) Fuzzy stock selection using a new fuzzy ranking and weighting algorithm. Applied Mathematics and Computation 170: 144–157MATHCrossRefMathSciNetGoogle Scholar
  58. Unser M. (2000) Lower partial moments as measures of perceived risk: An experimental study. Journal of Economic Psychology 21: 253–280CrossRefGoogle Scholar
  59. Vercher E., Bermúdez J.D., Segura J.V. (2007) Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems 158: 769–782MATHCrossRefMathSciNetGoogle Scholar
  60. Watada J. (1997) Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication 13: 219–248MATHMathSciNetGoogle Scholar
  61. Yan W., Miao R., Li S. (2007) Multi-period semi-variance portfolio selection: Model and numerical solution. Applied Mathematics and Computation 194: 128–134CrossRefMathSciNetGoogle Scholar
  62. Zadeh L. (1965) Fuzzy sets. Information and Control 8: 338–353MATHCrossRefMathSciNetGoogle Scholar
  63. Zadeh L. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28MATHCrossRefMathSciNetGoogle Scholar
  64. Zhang W.G., Nie Z.K. (2004) On admissible efficient portfolio selection problem. Applied Mathematics and Computation 159: 357–371MATHCrossRefMathSciNetGoogle Scholar
  65. Zhang W.G., Wang Y.L., Chen Z.P., Nie Z.K. (2007) Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences 177: 2787–2801MATHCrossRefMathSciNetGoogle Scholar
  66. Zimmermann H.J. (1985) Fuzzy set theory and its applications. Kluwer Academic Publisher, BostonGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Economics and ManagementUniversity of Science and Technology BeijingBeijingChina

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