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 càdlàg 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.

Two references added

References in corpus (2)

• Dirichlet forms and semilinear elliptic equations with measure data
• L^p solutions of reflected BSDEs under monotonicity condition

Cited by in corpus (2)

• Reflected backward stochastic differential equations with jumps in time-dependent random convex domains
• Systems of semilinear parabolic variational inequalities with time-dependent convex obstacles