Stochastic Optimization and Coupling

Frank Yang and Kai Hao Yang
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Frank Yang: Department of Economics, Harvard University
Kai Hao Yang: School of Management, Yale University

No 2506, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 104 pages
Date: 2026-03-12
New Economics Papers: this item is included in nep-des and nep-mic
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