PUB - Publikationen an der Universität Bielefeld

We consider the optimal stopping problem with non-linear ƒ-expectation (induced by a BSDE) without making any regularity assumptions on the reward process ξ. We show that the value family can be aggregated by an optional process *Y* . We characterize the process *Y* as the $\mathcal{E}$^ƒ-Snell envelope of ξ. We also establish an infinitesimal characterization of the value process *Y* in terms of a Reflected BSDE with ξ as the obstacle. To do this, we first establish a comparison theorem for irregular RBS DEs. We give an application to the pricing of American options with irregular pay-off in an imperfect market model.