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Constrained optimal stopping, liquidity and effort
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Hobson, David and Zeng, Matthew (2022) Constrained optimal stopping, liquidity and effort. Stochastic Processes and their Applications, 150 . pp. 819-843. doi:10.1016/j.spa.2019.10.010 ISSN 0304-4149.
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Official URL: https://doi.org/10.1016/j.spa.2019.10.010
Abstract
In a classical optimal stopping problem in continuous time, the agent can choose any stopping time without constraint. Dupuis and Wang (Optimal stopping with random intervention times, Advances in Applied Probability, 34, 141--157, 2002) introduced a constraint on the class of admissible stopping times which was that they had to take values in the set of event times of an exogenous, time-homogeneous Poisson process. This can be thought of as a model of finite liquidity. In this article we extend the analysis of Dupuis and Wang to allow the agent to choose the rate of the Poisson process. Choosing a higher rate leads to a higher cost. Even for a simple model for the stopped process and a simple call-style payoff, the problem leads to a rich range of optimal behaviours which depend on the form of the cost function. Often the agent accepts the first offer --- if they are not going to accept an offer then there is no point in putting in effort to generate offers, and thus there may be no offers to accept or decline --- but for some set-ups this is not the case.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0304-4149 | ||||||||
Official Date: | August 2022 | ||||||||
Dates: |
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Volume: | 150 | ||||||||
Page Range: | pp. 819-843 | ||||||||
DOI: | 10.1016/j.spa.2019.10.010 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 6 November 2019 | ||||||||
Date of first compliant Open Access: | 5 November 2020 | ||||||||
Related URLs: | |||||||||
Open Access Version: |
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