{
  "abstract": "This paper presents a generic approach for establishing mean field game master equations, applicable whenever the mean field equilibrium can be characterized by a McKean-Vlasov forward-backward stochastic differential equation system. The core of our approach is a representation formula for the first-order Lions derivative of the decoupling field of this forward-backward SDE system. We then employ a bootstrap argument to recursively compute its higher-order derivatives. To demonstrate the method's versatility, we establish the local well-posedness for master equations in three distinct models: extended mean field games, mean field games with volatility control, and mean field games with a major player.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29132",
  "author_total": 3,
  "authors": [
    {
      "name": "Chenchen Mou"
    },
    {
      "name": "Jianfeng Zhang"
    },
    {
      "name": "Jianjun Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/288c79y0hy862.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29132",
  "fulltext_url": null,
  "id": "288c79y0hy862",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29132",
  "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.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7166646191",
  "pdf_url": "https://arxiv.org/pdf/2606.29132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/288c79y0hy862.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2606.29132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Local well-posedness of general mean field game master equations",
  "title_text": "Local well-posedness of general mean field game master equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/288c79y0hy862",
  "venue": "arXiv",
  "versions": []
}