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Distribution-Constrained Optimal Stopping

Forthcoming in Mathematical Finance

34 Pages Posted: 8 Jul 2017 Last revised: 10 Jul 2017

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Christopher Wells Miller

University of California, Berkeley - Department of Mathematics

Date Written: May 13, 2016

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 selection. 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.

Keywords: Robust hedging with a volatility outlook

Suggested Citation

Bayraktar, Erhan and Miller, Christopher Wells, Distribution-Constrained Optimal Stopping (May 13, 2016). Forthcoming in Mathematical Finance. Available at SSRN: https://ssrn.com/abstract=2785826

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Christopher Wells Miller

University of California, Berkeley - Department of Mathematics ( email )

970 Evans Hall
Berkeley, CA 94720
United States

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