On a stopping game in continuous time
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- by Erhan Bayraktar and Zhou Zhou PDF
- Proc. Amer. Math. Soc. 144 (2016), 3589-3596 Request permission
Abstract:
On a filtered probability space $(\Omega ,\mathcal {F},P,\mathbb {F}=(\mathcal {F}_t)_{0\leq t\leq T})$, we consider stopper-stopper games $\overline C:=\inf _{\boldsymbol {\rho }}\sup _{\tau \in \mathcal {T}} \mathbb {E}[U(\boldsymbol {\rho }(\tau ),\tau )]$ and $\underline C:=$ $\sup _{\boldsymbol {\tau }} \inf _{\rho \in \mathcal {T}}\mathbb {E}[U(\rho ,\boldsymbol {\tau } (\rho ))]$ in continuous time, where $U(s,t)$ is $\mathcal {F}_{s\vee t}$-measurable (this is the new feature of our stopping game), $\mathcal {T}$ is the set of stopping times, and $\boldsymbol {\rho },\boldsymbol {\tau }:\mathcal {T} \mapsto \mathcal {T}$ satisfy certain non-anticipativity conditions. We show that $\overline C=\underline C$, by converting these problems into a corresponding Dynkin game.References
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Additional Information
- Erhan Bayraktar
- Affiliation: Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, Michigan 48109
- MR Author ID: 743030
- ORCID: 0000-0002-1926-4570
- Email: erhan@umich.edu
- Zhou Zhou
- Affiliation: Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, Michigan 48109
- Address at time of publication: Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street SE, Minneapolis, Minnesota 55455
- MR Author ID: 1054203
- Email: zhouzhou@ima.umn.edu
- Received by editor(s): September 23, 2014
- Received by editor(s) in revised form: June 3, 2015, July 4, 2015, and July 24, 2015
- Published electronically: April 14, 2016
- Additional Notes: This research was supported in part by the National Science Foundation under grant DMS 0955463
- Communicated by: David Levin
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3589-3596
- MSC (2010): Primary 60G40, 93E20, 91A10, 91A60, 60G07
- DOI: https://doi.org/10.1090/proc/12910
- MathSciNet review: 3503728