Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem
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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.
KeywordsStochastic dominance Convex optimization Strassen theorem
Mathematics Subject Classification90C15 90C25
This work is supported by A*STAR Grant 1421200078 and MOE tier I Grant R-266-000-083-113.
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