Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise
Abstract
The present study improves the qualitative analysis of backward stochastic variational dynamics on a general complete filtered probability space, considered in the spirit of Liang, Lyons and Qian (2011). Our primary objective is to overcome a substantial limitation in the study of Bensoussan, Li and Yam (2018), where the boundedness condition imposed on the multivalued subdifferential operator excludes standard obstacle-type constraints and indicator functions of convex sets. We prove the existence and uniqueness of a strong càdlàg solution under the natural assumption that the driving proper lower semicontinuous convex function is merely bounded from below by an affine/quadratic function. Furthermore, we incorporate an oblique reflection governed by a time-dependent, uniformly positive definite symmetric matrix, in the spirit of the pioneering results of Gassous, Răşcanu and Rotenstein (2012, 2015).
Related
- On the existence of a weak martingale solution for a stochastic magnetohydrodynamics system with noise acting in the magnetic field
- Necessary and sufficient conditions for the martingale property of stochastic exponentials driven by multi-dimensional diffusions
- A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition
- Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion
- Backward and reflected backward stochastic differential equations under initial enlargement of Brownian filtrations
BibTeX
@misc{negruţ2026càdlàg,
title = {{Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise}},
author = {Andreea Negruţ and Aurel Răşcanu and Eduard Rotenstein},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06045},
eprint = {2609.06045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06045},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise
AU - Andreea Negruţ
AU - Aurel Răşcanu
AU - Eduard Rotenstein
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06045
UR - https://arxiv.org/abs/2609.06045
AB - The present study improves the qualitative analysis of backward stochastic variational dynamics on a general complete filtered probability space, considered in the spirit of Liang, Lyons and Qian (2011). Our primary objective is to overcome a substantial limitation in the study of Bensoussan, Li and Yam (2018), where the boundedness condition imposed on the multivalued subdifferential operator excludes standard obstacle-type constraints and indicator functions of convex sets. We prove the existence and uniqueness of a strong càdlàg solution under the natural assumption that the driving proper lower semicontinuous convex function is merely bounded from below by an affine/quadratic function. Furthermore, we incorporate an oblique reflection governed by a time-dependent, uniformly positive definite symmetric matrix, in the spirit of the pioneering results of Gassous, Răşcanu and Rotenstein (2012, 2015).
ER -