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Journal of Optimization Theory and Applications

, Volume 178, Issue 3, pp 726–742 | Cite as

Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem

  • William B. Haskell
  • Alejandro Toriello
Article
  • 64 Downloads

Abstract

We use the Strassen theorem to solve stochastic optimization problems with stochastic dominance constraints. First, we show that a dominance-constrained problem on general probability spaces can be expressed as an infinite-dimensional optimization problem with a convenient representation of the dominance constraints provided by the Strassen theorem. This result generalizes earlier work which was limited to finite probability spaces. Second, we derive optimality conditions and a duality theory to gain insight into this optimization problem. Finally, we present a computational scheme for constructing finite approximations along with a convergence rate analysis on the approximation quality.

Keywords

Stochastic dominance Convex optimization Strassen theorem 

Mathematics Subject Classification

90C15 90C25 

Notes

Acknowledgements

This work is supported by A*STAR Grant 1421200078 and MOE tier I Grant R-266-000-083-113.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National University of SingaporeSingaporeSingapore
  2. 2.Georgia Institute of TechnologyAtlantaUSA

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