Stochastic Optimization and Coupling

Frank Yang; Kai Hao Yang

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arXiv · 2603.11448

Stochastic Optimization and Coupling

Frank Yang·Kai Hao Yang

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Abstract

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four properties are equivalent for any such order: (i) the test function cone is closed under pointwise minimum, (ii) the value function is affine, (iii) the solution correspondence has a convex graph with decomposable extreme points, and (iv) every ordered pair of measures admits an order-preserving coupling. As corollaries, we derive the extreme and exposed point properties involving integral stochastic orders such as multidimensional mean-preserving spreads and stochastic dominance. Applying these results, we generalize Blackwell's theorem by completely characterizing the comparisons of experiments that admit two equivalent descriptions -- through instrumental values and through information technologies. We also show that these results immediately yield new insights into information design, mechanism design, and decision theory.

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Frank Yang, Kai Hao Yang. 2026-03-12. Stochastic Optimization and Coupling. https://arxiv.org/abs/2603.11448

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