Reflected BSDEs in time-dependent convex regions

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