Robust stochastic dominance and its application to risk-averse optimization

  • Darinka DentchevaEmail author
  • Andrzej Ruszczyński
Full Length Paper Series B


We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconvex case, we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem.


Robust preferences Stochastic order Stochastic dominance constraints Risk constraints Semi-infinite optimization 

Mathematics Subject Classification (2000)

90C15 90C46 90C48 46N10 60E15 


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Copyright information

© Springer and Mathematical Programming Society 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Management Science and Information SystemsRutgers UniversityPiscatawayUSA

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