论文标题
阴影措施的潜力
The potential of the shadow measure
论文作者
论文摘要
众所周知，给定两个概率指标$μ$和$ν$在$ \ mathbb {r} $上按凸顺序订购时，这些边际有一个离散的时间martingale。已知几种解决方案（例如，关于布朗运动中的Skorokhod嵌入问题的文献）。但是，如果我们补充要求martingale应最大程度地减少其起始和完成位置的某些功能的预期价值，那么问题就变得更加困难。 Beiglböckand Juillet（Ann。prob。44（2016）42-106）引入了阴影措施，该措施诱导了Martingale耦合家族，并解决了一类双变量目标功能的最佳Martingale运输问题。在本文中，我们通过提供阴影措施的明确结构来扩展其（存在和独特性）结果，并作为应用程序提供了简单的证明其关联性。
It is well known that given two probability measures $μ$ and $ν$ on $\mathbb{R}$ in convex order there exists a discrete-time martingale with these marginals. Several solutions are known (for example from the literature on the Skorokhod embedding problem in Brownian motion). But, if we add a requirement that the martingale should minimise the expected value of some functional of its starting and finishing positions then the problem becomes more difficult. Beiglböck and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the shadow measure which induces a family of martingale couplings, and solves the optimal martingale transport problem for a class of bivariate objective functions. In this article we extend their (existence and uniqueness) results by providing an explicit construction of the shadow measure and, as an application, give a simple proof of its associativity.
