Optimal stopping with f-expectations: The irregular case

We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the reward process xi. We show that the value family can be aggregated by an optional process Y . We characterize the process Y as the Ef-Snell envelope of xi. We also establish an infinitesimal characterization of the value process Y in terms of a Reflected BSDE with xi 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.