Reflected BSDEs in non-convex domains

TL;DR

This paper proves the existence and uniqueness of reflected backward stochastic differential equations in certain non-convex domains, extending the theory to weaker geometric conditions and linking it to martingale theory on manifolds.

Contribution

It introduces well-posedness results for reflected BSDEs in non-convex, star-shaped domains under weaker assumptions than convexity, in both Markovian and general frameworks.

Findings

Well-posedness established in non-convex domains with star-shaped properties

Connections made between reflected BSDEs and martingales on manifolds

Results applicable under H"older continuity and small data assumptions

Abstract

This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian framework with H\"older-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.