Paper
Stochastic Optimization and Coupling
Authors
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.11448v1</id>\n <title>Stochastic Optimization and Coupling</title>\n <updated>2026-03-12T02:17:09Z</updated>\n <link href='https://arxiv.org/abs/2603.11448v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.11448v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='econ.TH'/>\n <category scheme='http://arxiv.org/schemas/atom' term='math.PR'/>\n <published>2026-03-12T02:17:09Z</published>\n <arxiv:comment>103 pages, 4 figures</arxiv:comment>\n <arxiv:primary_category term='econ.TH'/>\n <author>\n <name>Frank Yang</name>\n </author>\n <author>\n <name>Kai Hao Yang</name>\n </author>\n </entry>"
}