We formulate a notion of doubly reflected BSDE in the case where the barriers xi and zeta do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where xi is right upper-semicontinuous and...

We formulate a notion of doubly reflected BSDE in the case where the barriers xi and zeta do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where xi is right upper-semicontinuous and...

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 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....

In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate...

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward-backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the...

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward-backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the...

In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization prob- lem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).