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PreprintCC BY-SA 4.0arXiv

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

  • Youssef Ouknine
  • Badr Elmansouri
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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.

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Cite

BibTeXRIS
BibTeX
@misc{ouknine2026reflected,
  title = {{Reflected BSDEs under random horizons: Sharp support criteria, irregular reflection, and Cox reconstruction}},
  author = {Youssef Ouknine and Badr Elmansouri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31988},
  eprint = {2610.31988},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31988},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Reflected BSDEs under random horizons: Sharp support criteria, irregular reflection, and Cox reconstruction
AU  - Youssef Ouknine
AU  - Badr Elmansouri
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31988
UR  - https://arxiv.org/abs/2610.31988
AB  - 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.
ER  -