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Stochastic Optimization and Coupling

Author

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  • Frank Yang
  • Kai Hao Yang

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.

Suggested Citation

  • Frank Yang & Kai Hao Yang, 2026. "Stochastic Optimization and Coupling," Papers 2603.11448, arXiv.org.
    • Handle: RePEc:arx:papers:2603.11448
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    References listed on IDEAS

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