论文标题
Supermartingale Brenier的定理，具有全界限的约束
Supermartingale Brenier's Theorem with full-marginals constraint
论文作者
论文摘要
我们明确地构建了fr {é} chet-hoeffding耦合的超级智能版本，并与无限的许多边缘约束。这扩展了Henry-Labordere等人的结果。在Martingale环境中获得。我们的构建基于马尔可夫一期最佳超级智能耦合的迭代。在极限上，随着迭代的数量进入无限，我们获得了一个纯粹的跳跃过程，该过程属于Carr等人引入的局部L {é} Vy模型的家族。我们表明，构造的过程解决了特定的依赖路径依赖性成本函数系列的连续时间超级最佳运输问题。在以下三种情况下提供了明确的计算：统一的情况，Bachelier模型和几何布朗运动案例。
We explicitly construct the supermartingale version of the Fr{é}chet-Hoeffding coupling in the setting with infinitely many marginal constraints. This extends the results of Henry-Labordere et al. obtained in the martingale setting. Our construction is based on the Markovian iteration of one-period optimal supermartingale couplings. In the limit, as the number of iterations goes to infinity, we obtain a pure jump process that belongs to a family of local L{é}vy models introduced by Carr et al. We show that the constructed processes solve the continuous-time supermartingale optimal transport problem for a particular family of path-dependent cost functions. The explicit computations are provided in the following three cases: the uniform case, the Bachelier model and the Geometric Brownian Motion case.
