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The shape of the value function under Poisson optimal stopping
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Hobson, David (David G.) (2021) The shape of the value function under Poisson optimal stopping. Stochastic Processes and their Applications, 133 . pp. 229-246. doi:10.1016/j.spa.2020.12.001 ISSN 0304-4149.
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Official URL: http://dx.doi.org/10.1016/j.spa.2020.12.001
Abstract
In a classical problem for the stopping of a diffusion process , where the goal is to maximise the expected discounted value of a function of the stopped process , maximisation takes place over all stopping times . In a Poisson optimal stopping problem, stopping is restricted to event times of an independent Poisson process. In this article we consider whether the resulting value function (where the supremum is taken over stopping times taking values in the event times of an inhomogeneous Poisson process with rate ) inherits monotonicity and convexity properties from . It turns out that monotonicity (respectively convexity) of in depends on the monotonicity (respectively convexity) of the quantity rather than . Our main technique is stochastic coupling.
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): | Poisson processes , Optimal stopping (Mathematical statistics) , Diffusion processes, Monotonic functions, Convex functions | ||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
Publisher: | Elsevier Science BV | ||||||||
ISSN: | 0304-4149 | ||||||||
Official Date: | March 2021 | ||||||||
Dates: |
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Volume: | 133 | ||||||||
Page Range: | pp. 229-246 | ||||||||
DOI: | 10.1016/j.spa.2020.12.001 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 10 December 2020 | ||||||||
Date of first compliant Open Access: | 5 December 2021 |
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