Abstract

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.

中文翻译：

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具有域约束的运输计划

摘要

本文重点介绍了假设the具有有限二次方差的mar最优运输问题。首先，我们给出一个结果，表征除了给定初始和最终边际之外，满足一些凸传输约束的概率测度的存在。提供了几种应用程序：具有不确定性波动的mar测量，具有容量约束的最佳运输以及有时间限制的Skorokhod嵌入。接下来，我们将此结果扩展到多边际约束。最后，我们考虑带约束的最优运输问题，并获得其Kantorovich对偶性。这个结果的推论是单调性原理，它给出了识别优化器的几何方法。