Planar Obliquely Reflected BSVIs on General Filtered Spaces: Non-Symmetric Rotation Fields and Associated Control Problems
Abstract
We prove existence and uniqueness of a càdlàg solution to a planar backward stochastic variational inequality on a general complete filtered probability space, driven by a square integrable martingale, which may have jumps. The multivalued term is the exterior normal cone operator of a bounded uniformly convex planar domain, and the reflection direction is generated by a time-dependent non-symmetric rotation field. The non-symmetry creates a first-order tangential boundary term that destroys the standard monotonicity and quadratic contraction estimates, used in the symmetric oblique-reflection theory. We overcome this obstruction by constructing an explicit symmetric two-point kernel with state dependent coefficients, whose boundary derivative cancels the leading tangential contribution. A weighted martingale-exponential estimate then controls the second order defect and the jump terms. Under suitable geometric and quantitative compatibility constraints, we obtain the unique strong càdlàg solution. We also formulate associated control problems for the rotation angle and prove existence of an optimal control in a compact class of bounded-rate angle paths.
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BibTeX
@misc{negruţ2026planar,
title = {{Planar Obliquely Reflected BSVIs on General Filtered Spaces: Non-Symmetric Rotation Fields and Associated Control Problems}},
author = {Andreea Negruţ and Aurel Răşcanu and Eduard Rotenstein},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05723},
eprint = {2609.05723},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05723},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Planar Obliquely Reflected BSVIs on General Filtered Spaces: Non-Symmetric Rotation Fields and Associated Control Problems
AU - Andreea Negruţ
AU - Aurel Răşcanu
AU - Eduard Rotenstein
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05723
UR - https://arxiv.org/abs/2609.05723
AB - We prove existence and uniqueness of a càdlàg solution to a planar backward stochastic variational inequality on a general complete filtered probability space, driven by a square integrable martingale, which may have jumps. The multivalued term is the exterior normal cone operator of a bounded uniformly convex planar domain, and the reflection direction is generated by a time-dependent non-symmetric rotation field. The non-symmetry creates a first-order tangential boundary term that destroys the standard monotonicity and quadratic contraction estimates, used in the symmetric oblique-reflection theory. We overcome this obstruction by constructing an explicit symmetric two-point kernel with state dependent coefficients, whose boundary derivative cancels the leading tangential contribution. A weighted martingale-exponential estimate then controls the second order defect and the jump terms. Under suitable geometric and quantitative compatibility constraints, we obtain the unique strong càdlàg solution. We also formulate associated control problems for the rotation angle and prove existence of an optimal control in a compact class of bounded-rate angle paths.
ER -