Mathematical Approaches for Fuzzy Portfolio Selection Problems with Normal Mixture Distributions

1. Bawa, V.S., Lindenberg, E.B.: Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics 5, 189–200 (1977)

   Article  Google Scholar 

2. Bilbao-Terol, A., Perez-Gladish, B., Arenas-Parra, M., Rodriguez-Uria, M.V.: Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation 173, 251–264 (2006)

   Article  MATH  MathSciNet  Google Scholar 

3. Carlsson, C., Fuller, R., Majlender, P.: A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 131, 12–21 (2002)

   MathSciNet  Google Scholar 

4. Dinkelbach, W.: On nonlinear fractional programming. Management Science 13, 492–498 (1967)

   Article  MathSciNet  Google Scholar 

5. Elton, E.J., Gruber, M.J.: Modern Portfolio Theory and Investment Analysis. Wiley, New York (1995)

   Google Scholar 

6. Guo, P., Tanaka, H.: Possibility data analysis and its application to portfolio selection problems. Fuzzy Economic Rev. 3, 3–23 (1998)

   Google Scholar 

7. Hasuike, T., Ishii, H.: Probability maximization model of portfolio selection problem under ambiguity. Central European Journal of Operational Research (to appear)

   Google Scholar 

8. Hasuike, T., Katagiri, H., Ishii, H.: Portfolio selection problems with random fuzzy variable returns. In: Proceedings of IEEE International Conference on Fuzzy Systems 2007, pp. 416–421 (2007)

   Google Scholar 

9. Hasuike, T., Katagiri, H., Ishii, H.: Probability Maximization Model of 0-1 Knapsack Problem with Random Fuzzy Variables. In: Proceedings of 2008 IEEE World Congress in Computing Intelligence (WCCI 2008), IEEE International Conference on Fuzzy Systems 2008, pp. 548–554 (2008)

   Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

11. Hung, X.: Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research 180, 396–405 (2007)

    Article  MathSciNet  Google Scholar 

12. Inuiguchi, M., Ramik, J.: Possibilisitc 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 (2000)

    Article  MATH  MathSciNet  Google Scholar 

13. Inuiguchi, M., Tanino, T.: Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems 115, 83–92 (2000)

    Article  MATH  MathSciNet  Google Scholar 

14. Katagiri, H., Ishii, H., Sakawa, M.: On fuzzy random linear knapsack problems. Central European Journal of Operations Research 12(1), 59–70 (2004)

    MATH  MathSciNet  Google Scholar 

15. Katagiri, H., Sakawa, M., Ishii, H.: A study on fuzzy random portfolio selection problems using possibility and necessity measures. Scientiae Mathematicae Japonicae 65(2), 361–369 (2005)

    MathSciNet  Google Scholar 

16. Konno, H.: Piecewise linear risk functions and portfolio optimization. Journal of Operations Research Society of Japan 33, 139–156 (1990)

    MATH  MathSciNet  Google Scholar 

17. Konno, H., Shirakawa, H., Yamazaki, H.: A mean-absolute deviation-skewness portfolio optimization model. Annals of Operations Research 45, 205–220 (1993)

    Article  MATH  MathSciNet  Google Scholar 

18. Lai, H.C., Wu, S.Y.: On linear semi-infinite programming problems: an algorithm. Numerical Functional Analysis and Optimization 13, 287–304 (1992)

    Article  MATH  MathSciNet  Google Scholar 

19. Luenberger, D.G.: Investment Science. Oxford Univ. Press, Oxford (1997)

    Google Scholar 

20. Markowitz, H.: Portfolio Selection. Wiley, New York (1959)

    Google Scholar 

21. McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques & Tools. Princeton University Press, Princeton (2005)

    MATH  Google Scholar 

22. Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. Journal of Risk 2(3), 1–21 (2000)

    Google Scholar 

23. Steinbach, M.C.: Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM Review 43(1), 31–85 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

26. Watada, J.: Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Math. Pub. 13, 219–248 (1997)

    MATH  MathSciNet  Google Scholar 

Download references