{
  "abstract": "We study the superhedging of American claims with an irregular optional payoff process $ξ$ over the full set $\\mathcal{M}(X)$ of equivalent local martingale measures of a locally bounded market. We show that a process which is a strong optional supermartingale of class (D) under every $Q\\in\\mathcal{M}(X)$, with no bound from either side, decomposes as $S=S_0+\\int H\\,dX-A-C_-$, with a common integrand $H$, a right-continuous increasing process $A$ and a purely discontinuous increasing process $C$ given explicitly by the right jumps of $S$. For the robust Snell envelope this yields the superhedging duality $p_0(ξ)=\\sup_{Q}\\sup_τE^Q[ξ_τ]$ with an explicit optimal strategy and no regularity of $ξ$ in time. Unbounded payoffs are covered when $\\{ξ_τ\\}$ is uniformly integrable jointly over measures and stopping times, or when $|ξ|$ is dominated by a traded uniformly integrable martingale. For payoffs bounded below, the price is attained by wealth bounded below by a constant. For payoffs unbounded below this can fail, already in a complete market, and the price is attained once the constant bound is replaced by $-M$, with $M$ a traded martingale dominating $|ξ|$. In an incomplete Brownian market we study the associated reflected BSDE with an optional obstacle and a Lipschitz driver depending on the value. We prove existence and uniqueness of the minimal supersolution, a representation at stopping times, comparison and an equivalent dynamic minimality condition, for bounded data and for data dominated by a traded martingale. For a European-type obstacle, the Skorokhod conditions on the total regulator hold for some supersolution if and only if the terminal claim is attainable by a bounded wealth process; so in an incomplete market some data admit no supersolution satisfying them, while the right-jump regulator always satisfies its contact condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05116",
  "author_total": 3,
  "authors": [
    {
      "name": "Siham Bouhadou"
    },
    {
      "name": "Imade Fakhouri"
    },
    {
      "name": "Youssef Ouknine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cby5t9vbp0r0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05116",
  "fulltext_url": null,
  "id": "1cby5t9vbp0r0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05116",
  "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.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cby5t9vbp0r0.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Minimal Reflected BSDEs and Superhedging of Irregular American Claims",
  "title_text": "Minimal Reflected BSDEs and Superhedging of Irregular American Claims",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/1cby5t9vbp0r0",
  "venue": "arXiv",
  "versions": []
}