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Randomised rules for stopping problems
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Hobson, David (David G.) and Zeng, Matthew (2020) Randomised rules for stopping problems. Journal of Applied Probability, 57 (3). pp. 981-1004. doi:10.1017/jpr.2020.43 ISSN 0021-9002.
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Official URL: https://doi.org/10.1017/jpr.2020.43
Abstract
In a classical, continuous-time, optimal stopping problem, the agent chooses the best time to stop a stochastic process in order to maximise the expected discounted return. The agent can choose when to stop, and if at any moment they decide to stop, stopping occurs immediately with probability one. However, in many settings this is an idealistic oversimplification. Following Strack and Viefers we consider a modification of the problem in which stopping occurs at a rate which depends on the relative values of stopping and continuing: there are several different solutions depending on how the value of continuing is calculated. Initially we consider the case where stopping opportunities are constrained to be event times of an independent Poisson process. Motivated by the limiting case as the rate of the Poisson process increases to infinity, we also propose a continuous-time formulation of the problem where stopping can occur at any instant.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Optimal stopping (Mathematical statistics), Stochastic processes, Poisson processes | ||||||||
Journal or Publication Title: | Journal of Applied Probability | ||||||||
Publisher: | Applied Probability Trust | ||||||||
ISSN: | 0021-9002 | ||||||||
Official Date: | September 2020 | ||||||||
Dates: |
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Volume: | 57 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 981-1004 | ||||||||
DOI: | 10.1017/jpr.2020.43 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Applied Probability http://dx.doi.org/10.1017/jpr.2020.43 This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Applied Probability Trust 2020 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 11 September 2020 | ||||||||
Date of first compliant Open Access: | 4 March 2021 |
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