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

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    William B. Haskell

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Alejandro Toriello

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  1. William B. Haskell
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  2. Alejandro Toriello
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Correspondence to William B. Haskell.

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Communicated by René Henrion.

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Haskell, W.B., Toriello, A. Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem. J Optim Theory Appl 178, 726–742 (2018). https://doi.org/10.1007/s10957-018-1339-9

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  • DOI: https://doi.org/10.1007/s10957-018-1339-9

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