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

Source 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.