{
  "abstract": "We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the quadrant with nonsmooth max-type payoff \\(G(x_1,x_2)=x_1\\veeαx_2\\). The main novelty is a measure-valued variational formulation: the stopping gain \\(Γ=c+rG-\\mathcal LG\\) is shown to be a signed Radon measure whose singular component is supported on the kink diagonal \\(\\{x_1=αx_2\\}\\), and this component is computed explicitly. We prove that the value admits the killed-resolvent representation \\[ V=G-R_r^{\\mathcal C}Γ, \\] where the reflected diffusion is killed upon entry into the stopping set. This corrects the generally invalid unrestricted-resolvent formula. Under explicit monotonicity hypotheses, the stopping set has epigraph form, and the free boundary is characterized by a killed-potential trace condition. A verification theorem certifies locally Lipschitz candidate boundaries as optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21575",
  "author_total": 2,
  "authors": [
    {
      "name": "Louis Shuo Wang"
    },
    {
      "name": "Jiguang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hespazy5wjgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21575",
  "fulltext_url": null,
  "id": "0hespazy5wjgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21575",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7165659753",
  "pdf_url": "https://arxiv.org/pdf/2606.21575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hespazy5wjgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2606.21575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Nonsmooth Obstacles and Killed Resolvents in Reflected Stochastic Control",
  "title_text": "Nonsmooth Obstacles and Killed Resolvents in Reflected Stochastic Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0hespazy5wjgt",
  "venue": "arXiv",
  "versions": []
}