CANONICAL SUPERMARTINGALE COUPLINGS

• 成果类型: Article
• 署名作者: Nutz, Marcel; Stebegg, Florian
• 署名单位: Columbia University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1249
• 发表日期: 2018
• 页码: 3351-3398
• 关键词: martingale optimal transport; full marginals; Duality; superreplication; arbitrage; THEOREM; version; bounds

摘要

Two probability distributions p. and v in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Frechet coupling of classical transport and its symmetric counterpart, the antitone coupling, these can be characterized by order-theoretic minimality properties, as simultaneous optimal transports for certain classes of reward (or cost) functions, and through no-crossing conditions on their supports; however, our two couplings have asymmetric geometries. Remarkably, supermartingale optimal transport decomposes into classical and martingale transport in several ways.