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

William B. Haskell () and Alejandro Toriello ()
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William B. Haskell: National University of Singapore
Alejandro Toriello: Georgia Institute of Technology

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 3, 726-742

Abstract: 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; 90C15; 90C25 (search for similar items in EconPapers)
Date: 2018
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