A construction of the left-curtain coupling
A construction of the left-curtain coupling
复制标题
左帘联轴器的结构
DOI：
10.1214/22-ejp868
复制
发表时间：
2021
影响因子：
1.4
通讯作者：
Dominykas Norgilas
中科院分区：
文献类型：
--
作者：
D. Hobson;Dominykas Norgilas
在鞅最优运输（MOT）问题中，根据定律$\mu$分布的质量被运输到定律$\nu$，以这种方式尊重鞅性质。Beiglbock和Juillet（On a problem of optimal transport under marginal martingale constraints，Annals of Probability，44（1）：42-106，2016）介绍了MOT问题的一种解决方案，他们将其命名为左帘耦合。左帘耦合已经被广泛研究，并被证明有许多应用，包括鞅不等式和美式期权的模型独立定价。Beiglb“ock和Juillet证明了存在性和唯一性，证明了一族代价函数的最优性，并证明了当$\mu$是连续分布时，x$处的质量映射到至多两个点之一，给出了下函数和上函数。Henry-Labord\'ere和Touzi（Brenier定理的显式鞅版本，金融与随机，20：635-668，2016）表明，左帘耦合对于扩展的成本函数族是最优的，并在假设$\mu$和$\nu$是连续的情况下给出了上函数和下函数的构造，以及进一步简化的技术性假设。本文在凸序任意中心测度的一般情况下构造了这些上、下函数，从而给出了左帘耦合的完整构造。在$\mu$有原子的情况下，这些上、下函数将在提升鞅的意义上进行解释。
In a martingale optimal transport (MOT) problem mass distributed according to the law $\mu$ is transported to the law $\nu$ in such a way that the martingale property is respected. Beiglb\"ock and Juillet (On a problem of optimal transport under marginal martingale constraints, Annals of Probability, 44(1):42-106, 2016) introduced a solution to the MOT problem which they baptised the left-curtain coupling. The left-curtain coupling has been widely studied and shown to have many applications, including to martingale inequalities and the model-independent pricing of American options. Beiglb\"ock and Juillet proved existence and uniqueness, proved optimality for a family of cost functions, and proved that when $\mu$ is a continuous distribution, mass at $x$ is mapped to one of at most two points, giving lower and upper functions. Henry-Labord\`ere and Touzi (An explicit martingale version of Brenier`s theorem, Finance and Stochastics, 20:635-668, 2016) showed that the left-curtain coupling is optimal for an extended family of cost functions and gave a construction of the upper and lower functions under an assumption that $\mu$ and $\nu$ are continuous, together with further simplifying assumptions of a technical nature. In this article we construct these upper and lower functions in the general case of arbitrary centred measures in convex order, and thereby give a complete construction of the left-curtain coupling. In the case where $\mu$ has atoms these upper and lower functions are to be interpreted in the sense of a lifted martingale.
影响因子：
3.1
作者：
Beiglboeck, Mathias;Cox, Alexander M. G.;Huesmann, Martin
通讯作者：
Huesmann, Martin