Fuzzy Mathematical Programming for Portfolio Management

  • Teresa León
  • Vicente Liern
  • Enriqueta Vercher
Part of the Contributions to Management Science book series (MANAGEMENT SC.)

Abstract

The classical portfolio selection problem was formulated by Markowitz in the 1950s as a quadratic programming problem in which the risk variance is minimized. Since then, many other models have been considered and their associated mathematical programming formulations can be viewed as dynamic, stochastic or static decision problems. In our opinion, the model formulation depends essentially on two factors: the data nature and the treatment given to the risk and return goals. In this communication, we consider several approaches to deal with the data uncertainty for different classical formulations of the portfolio problem. We make use of duality theory and fuzzy programming techniques to analyze the solutions provided by these approaches and to repair infeasible instances.

Keywords

Covariance Univer 

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References

  1. 1.
    Cooper, W. W., Lelas, V., Sueyoshi, T. (1997) Goal programming models and their duality relations for use in evaluating security portfolio and regression relations, European Journal of Operational Research 98 (1997), 431–443.CrossRefGoogle Scholar
  2. 2.
    Feinstein, C. D., Thapa, M. N. (1993) Notes: A reformulation of a Mean-Absolute Deviation Portfolio Optimization Model, Management Science 39 1552–1553.CrossRefGoogle Scholar
  3. 3.
    Konno, H., Yamazaki, H. (1991) Mean-absolute deviation portfolio optimization model and its applications Tokyo Stock Market, Management Science 37 519–531.CrossRefGoogle Scholar
  4. 4.
    León, T., Liern, V. (1998) Fuzzy methods and infeasible linear programs: an application to staff design problems, Fuzzy Economic Review 3 79–94.Google Scholar
  5. 5.
    León, T., Liern, V. (1999) A fuzzy method to repair infeasibility in linearly constrained problems, Fuzzy Sets and Systems (submitted).Google Scholar
  6. 6.
    Lorenzana, T., Márquez, N.S., Sardà, S. (1996) An approach to the problem of portfolio selection, Fuzzy Economic Review 1 119–134.Google Scholar
  7. 7.
    Markowitz, H. M. (1959) Portfolio selection: Efficient Diversification of Investments, John Wiley, New York.Google Scholar
  8. 8.
    Perold, A. (1984), Large Scale Portfolio Optimizations,Management Science 30 1143–1160.CrossRefGoogle Scholar
  9. 9.
    Sharpe, W. F. (1963) A Simplified Model for Portfolio Analysis, Management Science 9 277–293.Google Scholar
  10. 10.
    Speranza, M. G. (1993) Linear programming model for portfolio optimization, Finance 14 107–123.Google Scholar
  11. 11.
    Tanaka, H., Guo, P. (1999) Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research 114 115–126.CrossRefGoogle Scholar
  12. 12.
    Tanaka, H., Guo, P. (1999) Possibilistic data analysis and its application to portfolio selection problems, Fuzzy Economic Review 2 3–23.Google Scholar
  13. 13.
    Zimmermann, H. J. (1996) Fuzzy Set Theory Kluwer Academic Publishers, Boston.Google Scholar
  14. 14.
    Zenios, S. A., Kang, P. (1993) Mean-absolute deviation portfolio optimization for mortgage-backed securities. Annals of Operations Research, 45 433–450.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Teresa León
    • 1
  • Vicente Liern
    • 2
  • Enriqueta Vercher
    • 1
  1. 1.Dep. d’Estadística i Investigació OperativaUniversitat de ValènciaSpain
  2. 2.Dep. d’Economia Financera i MatemàticaUniversitat de ValènciaSpain

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