Geometry of distribution-constrained optimal stopping problems

• 成果类型: Article
• 署名作者: Beiglboeck, Mathias; Eder, Manu; Elgert, Christiane; Schmock, Uwe
• 署名单位: University of Vienna; Technische Universitat Wien
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0805-x
• 发表日期: 2018
• 页码: 71-101
• 关键词: martingale optimal transport; brownian-motion; times; EXISTENCE

摘要

We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times t of Brownian motion subject to the constraint that the distribution of t is a given probability mu. The methods work for a large class of cost processes. (At a minimum we need the cost process to be measurable and (F0 t) t= 0-adapted. Continuity assumptions can be used to guarantee existence of solutions.) We find that for many of the cost processes one can come up with, the solution is given by the first hitting time of a barrier in a suitable phase space. As a by-product we recover classical solutions of the inverse first passage time problem/ Shiryaev's problem.