Palczewski, J and Stettner, L (2014) Infinite horizon stopping problems with (nearly) total reward criteria. Stochastic Processes and their Applications, 124 (12). 3887 - 3920. ISSN 0304-4149
Abstract
We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump-diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014. Elsevier. Uploaded in accordance with the publisher's self-archiving policy. NOTICE: this is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 124(12),(2014) DOI:10.1016/j.spa.2014.07.009 |
Keywords: | General Markovian discounting; Infinite horizon; Non-uniformly ergodic Markov processes; Optimal stopping; Total reward |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Nov 2014 12:09 |
Last Modified: | 30 Jun 2020 14:49 |
Published Version: | http://dx.doi.org/10.1016/j.spa.2014.07.009 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.spa.2014.07.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:81218 |