Nonlinear optimal stopping and domineering claims
Abstract
We study nonlinear optimal stopping and domineering claims in a Brownian--Poisson filtration, under a nonlinear evaluation induced by a Lipschitz BSDE driver satisfying a comparison condition. A nonlinear domineering claim is a strong ℰf-martingale dominating the reward process at every stopping time. We first establish the existence of such claims for every optional reward in 𝒮2. For left-limited, right-upper semicontinuous rewards, we prove a local dual representation at every stopping time: the nonlinear optimal stopping value equals the essential infimum of the values of all domineering claims defined on the remaining stochastic interval. This infimum is attained by a claim constructed from the associated reflected BSDE. We further show that a global domineering claim attains the value at a prescribed stopping time if and only if the reflection processes have accumulated no increase up to that time, with the appropriate endpoint convention. When the reward is right-upper semicontinuous in ℰf-expectation and the family of contact times is nonempty, its essential infimum is optimal. Under strict comparison, we also establish a necessary contact condition for optimality. No convexity assumption on the driver is required.
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BibTeX
@misc{bouhadou2026nonlinear,
title = {{Nonlinear optimal stopping and domineering claims}},
author = {Siham Bouhadou and Oussama Lamhadoul and Youssef Ouknine},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07743},
eprint = {2611.07743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07743},
}
RIS
TY - UNPB
TI - Nonlinear optimal stopping and domineering claims
AU - Siham Bouhadou
AU - Oussama Lamhadoul
AU - Youssef Ouknine
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07743
UR - https://arxiv.org/abs/2611.07743
AB - We study nonlinear optimal stopping and domineering claims in a Brownian--Poisson filtration, under a nonlinear evaluation induced by a Lipschitz BSDE driver satisfying a comparison condition. A nonlinear domineering claim is a strong ℰ^f-martingale dominating the reward process at every stopping time. We first establish the existence of such claims for every optional reward in 𝒮^2. For left-limited, right-upper semicontinuous rewards, we prove a local dual representation at every stopping time: the nonlinear optimal stopping value equals the essential infimum of the values of all domineering claims defined on the remaining stochastic interval. This infimum is attained by a claim constructed from the associated reflected BSDE. We further show that a global domineering claim attains the value at a prescribed stopping time if and only if the reflection processes have accumulated no increase up to that time, with the appropriate endpoint convention. When the reward is right-upper semicontinuous in ℰ^f-expectation and the family of contact times is nonempty, its essential infimum is optimal. Under strict comparison, we also establish a necessary contact condition for optimality. No convexity assumption on the driver is required.
ER -