Reflected BSDEs in time-dependent convex regions

We prove the existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and càdlàg convex regions D={Dt;t∈[0,T]}D={Dt;t∈[0,T]}. We also show that the solution may be approximated by solutions of backward equations with reflection in appropriately defined discretizations of DD and by a modified penalization method. The approximation results are new even in the one-dimensional case.