{
  "abstract": "This paper studies the penalization method for a general class of time-inconsistent stopping problems. Inspired by some existing results on penalization for optimal stopping problems, we introduce the penalized PDE problem and the penalized control problem for time-inconsistent stopping problems, uncovering some interesting discrepancy stemming from the time-inconsistency. As the penalization tends to infinity, we develop some novel arguments to rigorously establish the local $W^{2,1}_{p}$ convergence results for the solution of the penalized PDE problem to a solution of the variational inequality associated to the time-inconsistent stopping problem. Under an additional concavity assumption, we further derive the convergence of the penalized time-inconsistent control problem to the time-inconsistent stopping problem. We revisit two examples of time-inconsistent stopping to numerically illustrate the convergence theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06997",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaodong Luo"
    },
    {
      "name": "Xiang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63avy863nn1mr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06997",
  "fulltext_url": null,
  "id": "63avy863nn1mr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06997",
  "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"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221055065",
  "pdf_url": "https://arxiv.org/pdf/2610.06997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63avy863nn1mr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Local $W^{2,1}_{p}$ convergence of penalization for time-inconsistent stopping problems",
  "title_text": "Local W^2,1_p convergence of penalization for time-inconsistent stopping problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/63avy863nn1mr",
  "venue": "arXiv",
  "versions": []
}