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 characterise the value function in terms of the dynamic programming equation, which turns out to be a fully non-linear partial differential equation of second order. Finally, we obtain a classical verification theorem and illustrate its applicability with examples.
This talk is based on a joint work with Stefan Ankirchner and Thomas Kruse.