Abstract
A new portfolio optimization model with triangular fuzzy numbers is proposed in this paper. The objective function is considered as maximizing fuzzy expected return of securities under the constraint that the risk will not be greater than a preset tolerable fuzzy number, where the expected return and risk of securities are described as triangular fuzzy numbers. By using the method of dominance possibility criterion, the portfolio optimization model is converted into its equivalent crisp linear programming problem. Finally an example is presented to illustrate the effectiveness of the proposed algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdelaziz, F.B., Aouni, B., Fayedh, R.E.: Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res. 177, 1811–1823 (2007)
Ammar, E.E.: On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Inf. Sci. 178, 468–484 (2008)
Arenas-Parra, M., Bilbao-Terol, A., RodrÃguez-UÅ„a, M.V.: A fuzzy goal programming approach to portfolio selection. Eur. J. Oper. Rese. 133, 287–297 (2001)
Bilbao-Terol, A., Pérez-Gladish, B., Arenas-Parra, M., RodrÃguez-UÅ„a, M.V.: Fuzzy compromise programming for portfolio selection. Appl. Math. Comput. 173, 251–264 (2006)
Black, F., Litterman, R.: Asset allocation: combining investor views with market equilibrium. Journal of Fixed Income 1, 7–18 (1991)
Yong, F., Shouyang, W.: Fuzzy Portfolio Optimization—Theory and Method. Higher Education Press, Beijing (2005)
Tanaka, H., Guo, P., Turksen, B.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111, 387–397 (2000)
Hirschberger, M., Qi, Y., Steuer, R.E.: Randomly generatting portfolio-selection covariance matrices with specified distributional characteristics. European J. of Operational Research 177, 1610–1625 (2007)
Huang, X.: Two new models for portfolio selecion with stochastic returns taking fuzzy information. Eur. J. Oper. Res. 180, 396–405 (2007)
Huang, X.: Minimax mean-variance models for fuzzy portfolio selection. Soft Comput. 15, 251–260 (2011)
Iskander, M.: Using different dominance criteria in stochastic fuzzy linear multiobjective programming— a case of fuzzy weighted objective function. Mathematical and Computer Modelling 37, 167–176 (2003)
Konno, H., Yamazaki, H.: Mean-absolute deviation portfolio optimization model and its application to Tolyo Stock Market. Management Scicence 37, 519–531 (1991)
Yongming, L.: Analysis of Fuzzy System. Science Press, Beijing (2005)
Markowitz, H.: Portfolio selection. Journal of Finance 7, 77–91 (1952)
Negi, D.S., Lee, E.S.: Possibitlity programming by the comparison of fuzzy numbers. Computers Mate. Applic. 25, 43–50 (1993)
Xiuguo, W., Wanhua, Q., Jichang, D.: Portfolio Selection Model with Fuzzy Coefficients. Fuzzy Systems and Mathematics 20, 109–118 (2006)
Zadeh, L.A.: Fuzzy sets. Inform. and Contr. 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, C., Jin, J. (2011). Fuzzy Portfolio Optimization Model with Fuzzy Numbers. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_68
Download citation
DOI: https://doi.org/10.1007/978-3-642-22833-9_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
eBook Packages: EngineeringEngineering (R0)