Abstract
The mixed portfolio selection problem studied in this paper corresponds to a situation of financial risk management in which some return rates are mathematically described by random variables and others are described by fuzzy numbers. Both Markowitz probabilistic model and a possibilistic portfolio selection model are generalized. A calculation formula for the optimal solution of the portfolio problem and a formula which gives the minimum value of the associated risk are proved.
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References
Altăr, M.: Teoria portofoliului. Academy of Economic Studies, Bucharest (2002)
Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst. 122, 315–326 (2001)
Carlsson, C., Fullér, R.: Fuzzy reasoning in decision making and optimization. Studies in Fuzziness and Soft Computing Series, vol. 82. Springer, Berlin (2002)
Carlsson, C., Fullér, R., Majlender, P.: A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets Syst. 131, 13–21 (2002)
Carlsson, C., Fullér, R., Majlender, P.: On possibilistic correlations. Fuzzy Sets Syst. 155, 425–445 (2005)
Dubois, D., Prade, H.: Fuzzy sets and systems: theory and applications. Academic Press, New York (1980)
Dubois, D., Prade, H.: Possibility theory. Plenum Press, New York (1988)
Fullér, R., Majlender, P.: On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst. 136, 363–374 (2003)
Georgescu, I.: Possibility theory and the risk. Springer, Heidelberg (forthcoming, 2012)
Huang, X.: Portfolio analysis. Springer, Heidelberg (2010)
Huang, X.: Portfolio selection with fuzzy returns. J. Intelligent and Fuzzy Systems 18, 384–390 (2007)
Huang, X.: Minimax mean–variance models for fuzzy portfolio selection. Soft Computing 15, 251–260 (2011)
Inuiguchi, M., Ramik, J.: Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst. 111, 3–28 (2000)
Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)
Tanaka, H., Guo, P., Türksen, I.B.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets Syst. 111, 387–397 (2000)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)
Wang, S., Zhu, S.: On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making 1, 361–377 (2002)
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Georgescu, I., Kinnunen, J. (2012). A Mixed Portfolio Selection Problem. In: Omatu, S., De Paz Santana, J., González, S., Molina, J., Bernardos, A., Rodríguez, J. (eds) Distributed Computing and Artificial Intelligence. Advances in Intelligent and Soft Computing, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28765-7_13
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DOI: https://doi.org/10.1007/978-3-642-28765-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28764-0
Online ISBN: 978-3-642-28765-7
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