{
  "abstract": "We study state-constrained stochastic control problems with a scalar surplus $R \\geq 0$. Controls for which the drift and volatility of $R$ vanish at zero define a lower-dimensional Hamilton-Jacobi-Bellman equation. Starting from control-wise state-constraint viscosity inequalities, we prove that the upper and lower limits of the interior value are a subsolution and a supersolution of this boundary equation. Terminal compatibility and comparison identify their common limit. We require one-sided bounds on positive surplus drift and generator growth, together with domination by boundary generators. For compact or coercive controls, these follow from a local lower bound and continuity of the boundary control set. For a smooth stochastic target value $w$, the transformation $R = Y - w(t,X)$ flattens the viable epigraph, and, under the stated hypotheses, the boundary control value supplies the Dirichlet datum. Applications include set-valued boundary controls, unbounded drift with quadratic costs, and redundant hedging instruments with a nonconstant target boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05687",
  "author_total": 3,
  "authors": [
    {
      "name": "Erhan Bayraktar"
    },
    {
      "name": "Haichuan Ding"
    },
    {
      "name": "Ibrahim Ekren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f7sckbb8yhn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05687",
  "fulltext_url": null,
  "id": "8f7sckbb8yhn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05687",
  "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/2610.05687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f7sckbb8yhn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05687"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Target-Generated Dirichlet Problems in State-Constrained Stochastic Control",
  "title_text": "Target-Generated Dirichlet Problems in State-Constrained Stochastic Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8f7sckbb8yhn9",
  "venue": "arXiv",
  "versions": []
}