De Angelis, T and Stabile, G (2019) On Lipschitz Continuous Optimal Stopping Boundaries. SIAM Journal on Control and Optimization, 57 (1). pp. 402-436. ISSN 0363-0129
Abstract
We obtain a probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space $[0,T]\times\mathbb{R}^d$, $d\ge 1$. To the best of our knowledge this is the only existing proof that relies exclusively upon stochastic calculus, all the other proofs making use of PDE techniques and integral equations. Thanks to our approach we obtain our result for a class of diffusions whose associated second order differential operator is not necessarily uniformly elliptic. The latter condition is normally assumed in the related PDE literature.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019, Society for Industrial and Applied Mathematics. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | optimal stopping; free boundary problems; Lipschitz free boundaries |
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 Dec 2018 11:47 |
Last Modified: | 25 Jun 2023 21:38 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/17M1113709 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139849 |