De Angelis, T, Merkulov, N and Palczewski, J orcid.org/0000-0003-0235-8746 (2022) On the value of non-Markovian Dynkin games with partial and asymmetric information. Annals of Applied Probability, 32 (3). pp. 1774-1813. ISSN 1050-5164
Abstract
We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general càdlàg measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyond the variational methods (based on PDEs) developed in the literature on Dynkin games in continuous time with partial/asymmetric information. Instead, we focus on a probabilistic and functional analytic approach based on the general theory of stochastic processes and Sion’s min-max theorem (Pacific J. Math. 8 (1958) 171–176). Our framework encompasses examples found in the literature on continuous time Dynkin games with asymmetric information and we provide counterexamples to show that our assumptions cannot be further relaxed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Institute of Mathematical Statistics. This is an author produced version of an article published in The Annals of Applied Probability. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | asymmetric information , Non-Markovian Dynkin games , Optimal stopping , partial information , predictable-jump processes , randomised stopping times , regular processes |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Aug 2021 14:07 |
Last Modified: | 15 Jul 2022 20:04 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/21-AAP1721 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:177068 |