{
  "abstract": "We consider the distribution-constrained optimal stopping problem $\\sup_{τ\\sim μ} \\mathbb E[B^*_τ]$, where $μ$ is a probability distribution on $\\mathbb R_+$, and $(B^*_t)$ denotes the running maximum of a standard Brownian motion. This problem was introduced in Beiglbock et al. (PTRF, 2018), where a monotonicity principle is used to establish the optimal stopping time as the hitting time of a specific boundary. In this paper, we characterize this boundary by a variational inequality. In the spirit of Cox et al. (PTRF, 2019), we provide a novel probabilistic representation for the variational inequality as a time-reversed optimal stopping problem. A key ingredient for proving the viscosity solution property and comparison principle is a quantitative estimate near the singular corner of the time-space domain, where the initial and boundary conditions are incompatible. We then prove the optimality of the resulting hitting time through a discrete-time Snell envelope construction and a stability argument for the associated stopping times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01585",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuoqing Deng"
    },
    {
      "name": "Xin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etj7zh959a58j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01585",
  "fulltext_url": null,
  "id": "etj7zh959a58j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01585",
  "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"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7216231313",
  "pdf_url": "https://arxiv.org/pdf/2610.01585",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etj7zh959a58j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01585",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01585"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Distribution-constrained maximum stopping of maximum type",
  "title_text": "Distribution-constrained maximum stopping of maximum type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/etj7zh959a58j",
  "venue": "arXiv",
  "versions": []
}