The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

• 成果类型: Article
• 署名作者: Cox, Alexander M. G.; Obloj, Jan; Touzi, Nizar
• 署名单位: University of Bath; University of Oxford; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0833-1
• 发表日期: 2019
• 页码: 211-259
• 关键词: viscosity solutions; Optimal Transport; maximum maximum; martingale; barrier; inequalities

摘要

We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time-space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions.