{
  "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 $\\mathcal{E}^f$-martingale dominating the reward process at every stopping time. We first establish the existence of such claims for every optional reward in $\\mathcal{S}^2$. 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 $\\mathcal{E}^f$-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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07743",
  "author_total": 3,
  "authors": [
    {
      "name": "Siham Bouhadou"
    },
    {
      "name": "Oussama Lamhadoul"
    },
    {
      "name": "Youssef Ouknine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4c2fbs5w5g4v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07743",
  "fulltext_url": null,
  "id": "f4c2fbs5w5g4v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07743",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4c2fbs5w5g4v.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07743"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Nonlinear optimal stopping and domineering claims",
  "title_text": "Nonlinear optimal stopping and domineering claims",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/f4c2fbs5w5g4v",
  "venue": "arXiv",
  "versions": []
}