Fuzzy Mathematical Programming for Portfolio Management
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.
KeywordsMembership Function Fuzzy Number Portfolio Selection Portfolio Management Portfolio Return
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- 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.León, T., Liern, V. (1999) A fuzzy method to repair infeasibility in linearly constrained problems, Fuzzy Sets and Systems (submitted).Google Scholar
- 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.Markowitz, H. M. (1959) Portfolio selection: Efficient Diversification of Investments, John Wiley, New York.Google Scholar
- 9.Sharpe, W. F. (1963) A Simplified Model for Portfolio Analysis, Management Science 9 277–293.Google Scholar
- 10.Speranza, M. G. (1993) Linear programming model for portfolio optimization, Finance 14 107–123.Google Scholar
- 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.Zimmermann, H. J. (1996) Fuzzy Set Theory Kluwer Academic Publishers, Boston.Google Scholar