Doubly Reflected BSDEs and non-linear Dynkin games: beyond right-continuity

We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ are completely irregular. Under a Mokobodzki-type condition, we show existence and uniqueness of the solution. When $\xi$ is... [ view full abstract ]

We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ are completely irregular. Under a Mokobodzki-type condition, we show existence and uniqueness of the solution. When $\xi$ is
right-upper-semicontinuous and $\zeta$ is right-lower-semicontinuous, the solution is characterized in terms of the value of a non-linear Dynkin game over stopping times.  In the general case where the barriers are completely irregular, the solution is related to the value of "an extension" of the previous non-linear game problem over a larger set of "stopping strategies" than the set of stopping times.