Non-Markovian optimal stopping problems and constrained BSDEs with jump

Marco Fuhrman (1) , Huyen Pham (2, 3) , Federica Zeni (1)

1 Dipartimento di Matematica "F. Brioschi"
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 CREST - Centre de Recherche en Économie et Statistique

We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing a stochastic integral having a one-jump point process as integrator and an (unknown) process with a sign constraint as integrand. This provides an alternative representation with respect to the classical one given by a reflected BSDE. The connection between the two BSDEs is also clarified. Finally, we prove that the value of the optimal stopping problem is the same as the value of an auxiliary optimization problem where the intensity of the point process is controlled.

Domaines: Probabilités [math.PR]

Marco Fuhrman, Huyen Pham, Federica Zeni. Non-Markovian optimal stopping problems and constrained BSDEs with jump. 2015. ⟨hal-01118143⟩