Mathematical Programming

, Volume 89, Issue 2, pp 217–232 | Cite as

On consistency of stochastic dominance and mean–semideviation models

  • Włodzimierz Ogryczak
  • Andrzej Ruszczyński


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.

Key words: decisions under risk – stochastic dominance – mean–risk models – portfolio optimization 
Mathematics Subject Classification (2000): 91B06, 90C15, 91B28 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Włodzimierz Ogryczak
    • 1
  • Andrzej Ruszczyński
    • 2
  1. 1.Warsaw University of Technology, Institute of Control and Computation Engineering, 00–665 Warsaw, Poland, e-mail:
  2. 2.Rutgers University, Department of Management Science and Information Systems, Piscataway, NJ 08854, USA, e-mail: rusz@rutcor.rutgers.eduUS

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