Abstract
The stochastic dominance (SD) is based on an axiomatic model of risk-averse preferences and therefore, the SD-efficiency is an important property of selected portfolios. As defined with a continuum of criteria representing some measures of failure in achieving several targets, the SD does not provide us with a simple computational recipe. While limiting to a few selected target values one gets a typical multiple criteria optimization model approximating the corresponding SD approach. Although, it is rather difficult to justify a selection of a few target values, this difficulty can be overcome with the effective use of fuzzy target values. While focusing on the first degree SD and extending the target membership functions to some monotonic utility functions we get the multiple criteria model which preserves the consistency with both the first degree and the second degree SD. Further applying the reference point methodology to the multiple criteria model and taking advantages of fuzzy chance specifications we get the method that allows to model interactively the preferences by fuzzy specification of the desired distribution. The model itself guarantees that every generated solution is efficient according to the SD rules.
The research was partially supported by the Ministry of Science and Information Society Technologies under grant 3T11C 005 27.
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References
Bawa, V.S.: Safety-first, stochastic dominance and optimal portfolio choice. J. Finan. Quant. Anal. 13, 252–271 (1978)
Krzemienowski, A., Ogryczak, W.: On extending the LP computable risk measures to account downside risk. Comput. Optimization and Appls. 32, 133–160 (2005)
Levy, H.: Stochastic dominance and expected utility: survey and analysis. Manage. Sci. 38, 555–593 (1992)
Lewandowski, A., Wierzbicki, A.P. (eds.): Aspiration Based Decision Support Systems — Theory, Software and Applications. Springer, Berlin (1989)
Mansini, R., Ogryczak, W., Speranza, M.G.: On LP solvable models for portfolio selection. Informatica 14, 37–62 (2003)
Markowitz, H.M.: Portfolio selection. J. Fin. 7, 77–91 (1952)
McNamara, J.R.: Portfolio selection using stochastic dominance criteria. Decision Sci. 29, 785–801 (1998)
Ogryczak, W.: Multiple criteria linear programming model for portfolio selection. Ann. Oper. Res. 97, 143–162 (2000)
Ogryczak, W.: Multiple criteria optimization and decisions under risk. Control & Cybernetics 31, 975–1003 (2002)
Ogryczak, W., Ruszczyński, A.: From stochastic dominance to mean-risk models: semideviations as risk measures. Eur. J. Oper. Res. 116, 33–50 (1999)
Ribeiro, R.A., Zimmermann, H.-J., Yager, R.R., Kacprzyk, J. (eds.): Soft Computing in Financial Engineering. Physica-Verlag, Heidelberg (1999)
Romaszkiewicz, A.: Portfolio selection with techniques of fuzzy and multicriteria optimization (in Polish). Ph.D. Thesis, Warsaw School of Economics (2006)
Rothschild, M., Stiglitz, J.E.: Increasing risk: I. A definition. J. Econ. Theory 2, 225–243 (1969)
Whitmore, G.A., Findlay, M.C. (eds.): Stochastic Dominance: An Approach to Decision–Making Under Risk. D.C. Heath, Lexington (1978)
Wierzbicki, A.P.: A mathematical basis for satisficing decision making. Math. Modelling 3, 391–405 (1982)
Yager, R.R., Filev, D.P.: Essentials of Fuzzy Modelling and Control. Wiley, Chichester (1994)
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Ogryczak, W., Romaszkiewicz, A. (2007). On Fuzzy Driven Support for SD-Efficient Portfolio Selection. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71618-1_64
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