Possibilistic Decision-Making Models for Portfolio Selection Problems

  • Peijun Guo
Part of the Intelligent Systems Reference Library book series (ISRL, volume 33)


The basic assumption for using probabilistic decision-making models for portfolio selection problems, such as Markowitz’s model, is that the situation of stock markets in future can be correctly reflected by security data in the past, that is, the mean and covariance of securities in future is similar to the past one. It is hard to ensure this kind of assumption for the real ever-changing stock markets. Possibilistic decision-making models for portfolio selection problems are based on possibility distributions, which are used to characterize experts’ knowledge. A possibility distribution is identified using the returns of securities associated with possibility grades provided by experts. Based on the obtained possibility distribution, we construct a possibilistic portfolio selection decision-making model as a quadratic programming problem. Because experts’ knowledge is very valuable, it is reasonable that possibilistic decision-making models are useful in real investment environment.


Stock Market Portfolio Selection Portfolio Return Possibility Distribution Portfolio Selection Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bilbao-Terol, A., Pérez-Gladish, B., Arenas-Parra, M., Rodríguez-Uría, M.V.: Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation 173, 251–264 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dantzig, G.B., Infanger, G.: Multi-stage stochastic linear programs for portfolio optimization. Annals of Operations Research 45, 59–76 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Fang, Y., Lai, K.K., Wang, S.Y.: Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research 175(2), 879–893 (2006)zbMATHCrossRefGoogle Scholar
  4. 4.
    Guo, P., Tanaka, H.: Decision analysis based on fused double exponential possibility distributions. European Journal of Operational Research 148, 467–479 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Guo, P., Zeng, D., Shishido, H.: Group decision with inconsistent knowledge. IEEE Transactions on SMC, Part A 32, 670–679 (2002)Google Scholar
  6. 6.
    Guo, P., Tanaka, H.: Possibilistic data analysis and its application to portfolio selection problems. Fuzzy Economic Review 3/2, 3–23 (1998)Google Scholar
  7. 7.
    Inuiguchi, M., Ramík, J.: 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 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Konno, H., Wijayanayake, A.: Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints. Journal of Global Optimization 22, 137–154 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Lacagnina, V., Pecorella, A.: A stochastic soft constraints fuzzy model for a portfolio selection problem. Fuzzy Sets and Systems 157, 1317–1327 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    León, T., Liern, V., Vercher, E.: Viability of infeasible portfolio selection problems: A fuzzy approach. European Journal of Operational Research 139, 178–189 (2002a)zbMATHCrossRefGoogle Scholar
  11. 11.
    León, T., Liern, V., Vercher, E.: Two fuzzy approaches for solving multi-objective decision problems. Computational Economics 19, 273–286 (2002b)zbMATHCrossRefGoogle Scholar
  12. 12.
    Li, D., Ng, W.L.: Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Mathematical Finance 10(3), 387–406 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Markowitz, H.M.: Portfolio Selection: Efficient Diversification of Investments. John Wiley, New York (1959)Google Scholar
  14. 14.
    Mossin, J.: Optimal multiperiod portfolio policies. Journal of Business 41(2), 215–229 (1968)CrossRefGoogle Scholar
  15. 15.
    Ortí, J.J., Sáez, J., Terceño, A.: On the treatment of uncertainty in portfolio selection. Fuzzy Economic Review 7, 59–80 (2002)Google Scholar
  16. 16.
    Tanaka, H., Guo, P.: Possibilistic Data Analysis for Operations Research. Physica-Verlag, Heidelberg (1999)zbMATHGoogle Scholar
  17. 17.
    Tanaka, H., Guo, P.: Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114, 115–126 (1999)zbMATHCrossRefGoogle Scholar
  18. 18.
    Tanaka, H., Guo, P., Turksen, I.B.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111, 387–397 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Yoshimoto, A.: The mean-variance approach to portfolio optimization subject to transaction costs. Journal of the Operational Research Society of Japan 39, 99–117 (1996)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Peijun Guo
    • 1
  1. 1.Faculty of Business AdministrationYokohama National UniversityHodogaya-KuJapan

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