Stochastic Optimization and Coupling
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915856486760448 |
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| author | Yang, Frank Yang, Kai Hao |
| author_facet | Yang, Frank Yang, Kai Hao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11448 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimization and Coupling Yang, Frank Yang, Kai Hao Theoretical Economics Probability 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. |
| title | Stochastic Optimization and Coupling |
| topic | Theoretical Economics Probability |
| url | https://arxiv.org/abs/2603.11448 |