Electronic Journal of Probability

Stopping with expectation constraints: 3 points suffice

Stefan Ankirchner, Nabil Kazi-Tani, Maike Klein, and Thomas Kruse

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We consider the problem of optimally stopping a one-dimensional regular continuous strong Markov process with a stopping time satisfying an expectation constraint. We show that it is sufficient to consider only stopping times such that the law of the process at the stopping time is a weighted sum of 3 Dirac measures. The proof uses recent results on Skorokhod embeddings in order to reduce the stopping problem to a linear optimization problem over a convex set of probability measures.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 66, 16 pp.

Received: 23 September 2018
Accepted: 29 April 2019
First available in Project Euclid: 28 June 2019

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Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J60: Diffusion processes [See also 58J65] 60B05: Probability measures on topological spaces

optimal stopping expectation constraint Skorokhod embedding problem one-dimensional strong Markov processes extreme points of sets of probability measures

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Ankirchner, Stefan; Kazi-Tani, Nabil; Klein, Maike; Kruse, Thomas. Stopping with expectation constraints: 3 points suffice. Electron. J. Probab. 24 (2019), paper no. 66, 16 pp. doi:10.1214/19-EJP309. https://projecteuclid.org/euclid.ejp/1561687599

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