Reflected backward stochastic differential equations with two optional barriers

Abstract

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove the existence and uniqueness of ${\mathbb{L}}^p$ solutions, $p\ge 1$, and show that the solutions may be approximated by a modified penalization method.