STABILITY OF THE WEAK MARTINGALE OPTIMAL TRANSPORT PROBLEM

• 成果类型: Article
• 署名作者: Beiglboeck, Mathias; Jourdain, Benjamin; Margheriti, William; Pammer, Gudmund
• 署名单位: University of Vienna; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1950
• 发表日期: 2023
• 页码: 5382-5412
• 关键词: brenier; bounds; COSTS; plans

摘要

While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also nonlinear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327-3405) for classical optimal transport, this corresponds to weak martingale optimal transport (WMOT).In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of the stretched Brownian motion and we derive a monotonicity principle for WMOT.