A review of credibilistic portfolio selection Article

First Online: 10 June 2009 DOI :
10.1007/s10700-009-9064-3

Cite this article as: Huang, X. Fuzzy Optim Decis Making (2009) 8: 263. doi:10.1007/s10700-009-9064-3
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 Arditti F.D. (1971) Another look at mutual fund performance. Journal of Financial and Quantitative Analysis 6: 909–912

CrossRef 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: 287–297

MATH CrossRef 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: 251–264

MATH CrossRef MathSciNet Bruckley J.J., Hayashi Y. (1994) Fuzzy genetic algorithm and applications. Fuzzy Sets and Systems 61: 129–136

CrossRef MathSciNet Bruckley J.J., Feruing T. (2000) Evolution algorithm solution to fuzzy problems: Fuzzy linear programming. Fuzzy Sets and Systems 109: 35–53

CrossRef MathSciNet Carlsson C., Fullér R., Majlender P. (2002) A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 131: 13–21

MATH CrossRef MathSciNet 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: 143–167

CrossRef 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: 384–390

CrossRef De Cooman G. (1997) Possibility theory I–III. International Journal of General Systems 25: 291–371

MATH CrossRef MathSciNet Dubois D., Prade H. (1988) Possibility theory: An approach to computerized processing of uncertainty. Plenum, New York

MATH Fama E. (1965) Portfolio analysis in a stable paretian market. Management Science 11: 404–419

CrossRef Gupta P., Mehlawat M.K., Saxena A. (2008) Asset portfolio optimization using fuzzy mathe matical programming. Information Sciences 178: 1734–1755

MATH CrossRef MathSciNet Holland J. (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

Huang, X. (2004). Portfolio selection with fuzzy returns. Proceedings of the Second Annual conference on Uncertainty (pp. 21–29). Qinhuangdao July 16–20.

Huang X. (2006) Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation 177: 500–507

MATH CrossRef MathSciNet Huang X. (2007a) Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research 180: 396–405

MATH CrossRef MathSciNet Huang X. (2007b) A new perspective for optimal portfolio selection with random fuzzy returns. Information Sciences 177: 5404–5414

MATH CrossRef MathSciNet Huang X. (2007c) Portfolio selection with fuzzy returns. Journal of Intelligent & Fuzzy Systems 18: 383–390

MATH Huang X. (2008a) Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics 217: 1–8

MATH CrossRef MathSciNet Huang X. (2008b) Risk curve and fuzzy portfolio selection. Computers and Mathematics with Applications 55: 1102–1112

MATH CrossRef MathSciNet Huang X. (2008c) Expected model for portfolio selection with random fuzzy returns. International Journal of General Systems 37: 319–328

MATH CrossRef MathSciNet Huang X. (2008d) Portfolio selection with a new definition of risk. European Journal of Operational Research 186: 351–357

MATH CrossRef MathSciNet Huang X. (2008e) Mean-entropy models for fuzzy portfolio selection. IEEE Transactions on Fuzzy Systems 16: 1096–1101

CrossRef Huang, X. (2008f). Minimax mean-variance models for fuzzy portfolio selection, Technical Report.

Huang, X. (2008g). Fuzzy minimax chance constrained models for portfolio selection, Technical Report.

Huang, X. (2008h). Mean-variance model for hybrid portfolio selection with randomness and fuzziness, Technical Report.

Ida M. (2002) Mean-variance portfolio optimization model with uncertain coefficients. Proceedings of IEEE International Conference on Fuzzy Systems 3: 1223–1226

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: 3–28

MATH CrossRef MathSciNet Katagiri H., Ishii H. (1999) Fuzzy portfolio selection problem. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 3: III-973–III-978

Kaufman A., Gupta M.M. (1985) Introduction to fuzzy arithmetic: Theory and applications. Van Nostrand Reinhold, New York

Klir G.J., Yuan B. (1995) Fuzzy sets and fuzzy logic: Theory and applications. Prentice-Hall, New Jersey

MATH Lacagnina V., Pecorella A. (2006) A stochastic soft constraints fuzzy model for a portfolio selection problem. Fuzzy Sets and Systems 157: 1317–1327

MATH CrossRef MathSciNet León T., Liern V., Vercher E. (2002) Viability of infeasible portfolio selection problems: A fuzzy approach. European Journal of Operational Research 139: 178–189

MATH CrossRef Li J., Xu J. (2009) A novel portfolio selection model in a hybrid uncertain environment. Omega 37: 439–449

CrossRef Li P., Liu B. (2008) Entropy of credibility distributions for fuzzy variables. IEEE Transactions on Fuzzy Systems 16: 123–129

CrossRef Li X., Liu B. (2007) Maximum entropy principle for fuzzy variable. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 15(Supp. 2): 43–52

CrossRef Lin C.C., Liu Y.T. (2008) Genetic algorithm for portfolio selection problems with minimum transaction lots. European Journal of Operational Research 185: 393–404

MATH CrossRef Liu B. (1998) Minimax chance constrained programming models for fuzzy decision systems. Information Sciences 112: 25–38

MATH CrossRef MathSciNet Liu B. (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg

MATH Liu B. (2004) Uncertainty theory: An introduction to its axiomatic foundations. Springer–Verlag, Berlin

MATH Liu B. (2006a) A survey of credibility theory. Fuzzy Optimization and Decision Making 5: 387–408

CrossRef MathSciNet Liu B. (2007) Uncertainty theory, 2nd edn. Springer–Verlag, Berlin

MATH Liu B., Iwamura K. (1998) Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems 94: 227–237

MATH CrossRef MathSciNet Liu B., Liu Y.K. (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10: 445–450

CrossRef Liu Y.K. (2006b) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Transactions on Fuzzy Systems 14: 295–304

CrossRef Markowitz H. (1952) Portfolio selection. Journal of Finance 7: 77–91

CrossRef Markowitz H. (1959) Portfolio selection: efficient diversification of investments. Wiley, New York

Nahmias S. (1978) Fuzzy variables. Fuzzy Sets and Systems 1: 97–110

MATH CrossRef MathSciNet 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: 527–534

Rahib H.A., Mustafa M. (2007) Fuzzy portfolio selection using genetic algorithm. Soft Computing—A Fusion of Foundations, Methodologies and Applications 11: 1157–1163

MATH Rom B.M., Ferguson K.W. (1994) Post-modern portfolio theory comes of age. Journal of Investing 3: 11–17

CrossRef Shoaf, J., & Foster, J. A. (1996). The efficient set GA for stock portfolios. Proceedings of the Decision Science Institute, Orlando (pp. 571–573).

Simkowitz M., Beedles W. (1978) Diversification in a three moment world. Journal of Financial and Quantitative Analysis 13: 927–941

CrossRef 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).

Tanaka H., Guo P. (1999) Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114: 115–126

MATH CrossRef Tanaka H., Guo P., Türksen B. (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111: 387–397

MATH CrossRef MathSciNet Tiryaki F., Ahlatcioglu M. (2005) Fuzzy stock selection using a new fuzzy ranking and weighting algorithm. Applied Mathematics and Computation 170: 144–157

MATH CrossRef MathSciNet Unser M. (2000) Lower partial moments as measures of perceived risk: An experimental study. Journal of Economic Psychology 21: 253–280

CrossRef Vercher E., Bermúdez J.D., Segura J.V. (2007) Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems 158: 769–782

MATH CrossRef MathSciNet Watada J. (1997) Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication 13: 219–248

MATH MathSciNet Yan W., Miao R., Li S. (2007) Multi-period semi-variance portfolio selection: Model and numerical solution. Applied Mathematics and Computation 194: 128–134

CrossRef MathSciNet Zadeh L. (1965) Fuzzy sets. Information and Control 8: 338–353

MATH CrossRef MathSciNet Zadeh L. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28

MATH CrossRef MathSciNet Zhang W.G., Nie Z.K. (2004) On admissible efficient portfolio selection problem. Applied Mathematics and Computation 159: 357–371

MATH CrossRef MathSciNet 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: 2787–2801

MATH CrossRef MathSciNet Zimmermann H.J. (1985) Fuzzy set theory and its applications. Kluwer Academic Publisher, Boston

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Authors and Affiliations 1. School of Economics and Management University of Science and Technology Beijing Beijing China