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2018 Optimal stopping and the sufficiency of randomized threshold strategies
Vicky Henderson, David Hobson, Matthew Zeng
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP125

Abstract

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.

Citation

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Vicky Henderson. David Hobson. Matthew Zeng. "Optimal stopping and the sufficiency of randomized threshold strategies." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP125

Information

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

zbMATH: 1390.60155
MathSciNet: MR3798241
Digital Object Identifier: 10.1214/18-ECP125

Subjects:
Primary: 60G40

JOURNAL ARTICLE
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