论文标题
熵Martingale的最佳运输和非线性定价对冲二重性
Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality
论文作者
论文摘要
本文的目的是在新颖的熵玛特宁格最佳运输问题（a）和相关的优化问题（b）之间发展出双重性。在（a）中，我们遵循Liero等人在熵最佳转运（EOT）原始问题中采用的方法。 “最佳的熵传输问题和正面措施之间的新的Hellinger-Kantorovic距离”，发明。数学。 2018年，但我们添加了Martingale最佳运输（MOT）理论的典型限制，即成本功能的最大功能是在Martingale概率措施上采取的，而不是有限的积极措施，例如Liero等人。不仅受到马山的约束，而且还因为我们承认限制性的惩罚条款$ \ Mathcal {d} _ {u} $，这可能没有差异公式。在问题（b）中，通过fenchel共轭与$ \ mathcal {d} _ {u} $相关联的目标函数不再是线性的，因为在ot或mot中。这导致了一个新颖的优化问题，该问题也将经济解释清晰地解释为非线性亚涉及价值。我们的理论使我们能够建立一个非线性鲁棒的定价对冲二元性，该双重性涵盖了广泛的已知稳健结果。我们还专注于Wasserstein引起的惩罚，我们研究二元性如何受惩罚术语的变化影响，特别关注情绪与MOT极端情况的融合。
The objective of this paper is to develop a duality between a novel Entropy Martingale Optimal Transport problem (A) and an associated optimization problem (B). In (A) we follow the approach taken in the Entropy Optimal Transport (EOT) primal problem by Liero et al. "Optimal entropy-transport problems and a new Hellinger-Kantorovic distance between positive measures", Invent. math. 2018, but we add the constraint, typical of Martingale Optimal Transport (MOT) theory, that the infimum of the cost functional is taken over martingale probability measures, instead of finite positive measures, as in Liero et al.. The Problem (A) differs from the corresponding problem in Liero et al. not only by the martingale constraint, but also because we admit less restrictive penalization terms $\mathcal{D}_{U}$, which may not have a divergence formulation. In Problem (B) the objective functional, associated via Fenchel conjugacy to the terms $\mathcal{D}_{U}$, is not any more linear, as in OT or in MOT. This leads to a novel optimization problem which also has a clear financial interpretation as a nonlinear subhedging value. Our theory allows us to establish a nonlinear robust pricing-hedging duality, which covers a wide range of known robust results. We also focus on Wasserstein-induced penalizations and we study how the duality is affected by variations in the penalty terms, with a special focus on the convergence of EMOT to the extreme case of MOT.
