A verification theorem for optimal stopping problems with expectation constraints

Stefan Ankirchner (1) , Maike Klein (1) , Thomas Kruse (2)

1 Institute for Mathematics
2 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]

We consider the problem of optimally stopping a continuous-time process with a stopping time satisfying a given expectation cost constraint. We show, by introducing a new state variable, that one can transform the problem into an unconstrained control problem and hence derive a dynamic programming principle. We characterize the value function in terms of the dynamic programming equation, which turns out to be an elliptic, fully non-linear partial differential equation of second order. We prove a classical verification theorem and illustrate its applicability with several examples.

Domaines: Mathématiques [math]

Stefan Ankirchner, Maike Klein, Thomas Kruse. A verification theorem for optimal stopping problems with expectation constraints. 2015. ⟨hal-01229024⟩