Distribution‐constrained optimal stopping. (7th February 2018)

• Record Type: Journal Article
• Authors: Bayraktar, Erhan; Miller, Christopher W.
• Is Part Of: Mathematical finance. Volume 29:Number 1(2019)
• Page Start: 368
• Page End: 406
• Publication Date: 2018-02-07
• Subjects: distribution constraints -- optimal stopping -- optimal control -- robust hedging with a volatility outlook -- state constraints; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12171
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely many atoms. In particular, we show that this problem can be converted to a finite sequence of state‐constrained optimal control problems with additional states corresponding to the conditional probability of stopping at each possible terminal time. The proof of this correspondence relies on a new variation of the dynamic programming principle for state‐constrained problems, which avoids measurable selections. We emphasize that distribution constraints lead to novel and interesting mathematical problems on their own, but also demonstrate an application in mathematical finance to model‐free superhedging with an outlook on volatility.