{
  "abstract": "We study a mean-field optimal stopping problem with an endogenous population-level shutdown. All remaining agents stop when the survival mass falls below a prescribed threshold. We recast the discontinuous objective as the singular, nonconvex constraint that the survival mass lie in $\\{0\\}\\cup[α,1]$. We prove the equivalence of strong and weak values via an approximation and the existence of an optimal rule via compactness and penalization. We also prove a dynamic programming principle. The value is continuous away from the critical boundary but may be discontinuous at the boundary itself. Under strict initial feasibility, finite-population values converge to the mean-field value. In the same regime, the laws of near-optimal empirical measures are tight and every mean-field optimizer admits a recovery sequence. At the threshold, however, finite-population convergence may fail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03277",
  "author_total": 3,
  "authors": [
    {
      "name": "Erhan Bayraktar"
    },
    {
      "name": "Ibrahim Ekren"
    },
    {
      "name": "Xihao He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gas29trcb522.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03277",
  "fulltext_url": null,
  "id": "6gas29trcb522",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03277",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7208787008",
  "pdf_url": "https://arxiv.org/pdf/2609.03277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gas29trcb522.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03277"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Mean-field optimal stopping with endogenous quantile cutoffs",
  "title_text": "Mean-field optimal stopping with endogenous quantile cutoffs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/6gas29trcb522",
  "venue": "arXiv",
  "versions": []
}