Reflected BSDEs under random horizons: Sharp support criteria, irregular reflection, and Cox reconstruction

Abstract

We study reduction and reconstruction of reflected backward stochastic differential equations (RBSDEs) across random horizons. We establish optional and predictable contact-measure transfer criteria by dual projection, prove a Cox survival identity for arbitrary integrable reflection measures (including atoms), and give a Brownian Cox reconstruction theorem with continuous obstacles and a converse within a specified reduction class. We also isolate componentwise minimality criteria for irregular obstacles and predictable reflection. The unresolved semimartingale and obstacle transport problems for general non-Cox invariance times are formulated as open questions rather than asserted as theorems. The paper distinguishes established results from conditional constructions.