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.
"Stopping with expectation constraints: 3 points suffice." Electron. J. Probab. 24 1 - 16, 2019. https://doi.org/10.1214/19-EJP309