Reflected BSDEs in time-dependent convex regions

TL;DR

This paper establishes existence, uniqueness, and approximation methods for reflected backward stochastic differential equations within time-dependent convex regions, extending previous results especially in the one-dimensional case.

Contribution

It introduces new approximation techniques for solutions of reflected BSDEs in time-dependent convex regions, including discretization and penalization methods.

Findings

Existence and uniqueness of solutions in time-dependent convex regions

Approximation of solutions via discretized reflected equations

Novel penalization method for one-dimensional cases

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.