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On a stopping game in continuous time


Authors: Erhan Bayraktar and Zhou Zhou
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
Published electronically: April 14, 2016
MathSciNet review: 3503728
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

Erhan Bayraktar
Affiliation: Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, Michigan 48109
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
Email: zhouzhou@ima.umn.edu

DOI: https://doi.org/10.1090/proc/12910
Keywords: A new type of optimal stopping game, non-anticipative stopping strategies, Dynkin games, saddle point
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
Article copyright: © Copyright 2016 American Mathematical Society

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