A verification theorem for optimal stopping problems with expectation constraints
Résumé
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]
Origine : Fichiers produits par l'(les) auteur(s)
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