On consistency of stochastic dominance and mean–semideviation models |
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| Authors: | Włodzimierz Ogryczak Andrzej Ruszczyński |
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| Institution: | (1) Warsaw University of Technology, Institute of Control and Computation Engineering, 00–665 Warsaw, Poland, e-mail: ogryczak@ia.pw.edu.pl, PL;(2) Rutgers University, Department of Management Science and Information Systems, Piscataway, NJ 08854, USA, e-mail: rusz@rutcor.rutgers.edu, US |
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| Abstract: | We analyze relations between two methods frequently used for modeling the choice among uncertain outcomes: stochastic dominance
and mean–risk approaches. New necessary conditions for stochastic dominance are developed. These conditions compare values
of a certain functional, which contains two components: the expected value of a random outcome and a risk term represented
by the central semideviation of the corresponding degree. If the weight of the semideviation in the composite objective does
not exceed the weight of the expected value, maximization of such a functional yields solutions which are efficient in terms
of stochastic dominance. The results are illustrated graphically.
Received: September 15, 1998 / Accepted: October 1, 2000?Published online December 15, 2000 |
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| Keywords: | : decisions under risk – stochastic dominance – mean– risk models – portfolio optimization |
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