Electronic Communications in Probability

Optimal stopping and the sufficiency of randomized threshold strategies

Vicky Henderson, David Hobson, and Matthew Zeng

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In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which the value associated to a stopping rule depends on the law of the stopped process. If this value is quasi-convex on the space of attainable laws then it is well known that it is sufficient to restrict attention to the class of threshold strategies. However, if the objective function is not quasi-convex, this may not be the case. We show that, nonetheless, it is sufficient to restrict attention to mixtures of threshold strategies.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 30, 11 pp.

Received: 3 August 2017
Accepted: 12 March 2018
First available in Project Euclid: 3 May 2018

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

optimal stopping threshold strategies randomised strategies

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Henderson, Vicky; Hobson, David; Zeng, Matthew. Optimal stopping and the sufficiency of randomized threshold strategies. Electron. Commun. Probab. 23 (2018), paper no. 30, 11 pp. doi:10.1214/18-ECP125. https://projecteuclid.org/euclid.ecp/1525312854

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