Reflected BSDEs in non-convex domains

Abstract

This paper establishes the well-posedness of reflected backward stochastic differential equations in non-convex domains that satisfy a weak version of the star-shaped property. The main results are established (i) in a Markovian framework with Hölder-continuous generator and terminal condition and (ii) in a general setting under a smallness assumption on the input data. We also investigate the connections between this well-posedness result and the theory of martingales on manifolds, which, in particular, illustrates the sharpness of some of our assumptions.