THE LEFT-CURTAIN MARTINGALE COUPLING IN THE PRESENCE OF ATOMS

• 成果类型: Article
• 署名作者: Hobson, David G.; Norgilas, Dominykas
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1450
• 发表日期: 2019
• 页码: 1904-1928
• 关键词: transport

摘要

Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the left-curtain martingale coupling of probability measures mu and nu and proved that, when the initial law mu is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law mu it is characterised by two appropriately defined lower and upper functions. As an application of this result, we derive the model-independent upper bound of an American put option. This extends recent results of Hobson and Norgilas (2017) on the atom-free case.