Stopping with expectation constraints: 3 points suffice

Stefan Ankirchner (1) , Nabil Kazi-Tani (2) , Maike Klein (1) , Thomas Kruse (3)

1 Institut für Mathematik
2 SAF - Laboratoire de Sciences Actuarielle et Financière
3 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]

We consider the problem of optimally stopping a one-dimensional continuous-time 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.

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Stefan Ankirchner, Nabil Kazi-Tani, Maike Klein, Thomas Kruse. Stopping with expectation constraints: 3 points suffice. 2017. ⟨hal-01525439⟩