{
  "abstract": "The research studies the extended mean-field anticipated forward-backward stochastic delayed differential equations with common noise (extended MF-AFBSDDEswCN) by expanding the domination-monotonicity conditions. We generalize the conditions from a linear setting to a nonlinear one by including nonlinear adjoint functions which are key to guaranteeing the well-posedness of extended MF-AFBSDDEswCN. Utilizing this broader well-posedness framework for extended MF-AFBSDDEswCN, combined with other refined analytical tools, we examine two classes of stochastic optimal control problems. These include a linear-convex problem and a linear-quadratic problem with input constraints that can be both time-dependent and random. Moreover, the control elements regarding the initial values are path-dependent, which will cause some essential difficulties. For each problem, we establish the existence and uniqueness of optimal controls and provide their explicit, closed-form representations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19779",
  "author_total": 1,
  "authors": [
    {
      "name": "Hao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jct6afqcgm7c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19779",
  "fulltext_url": null,
  "id": "5jct6afqcgm7c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19779",
  "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": "W7213611642",
  "pdf_url": "https://arxiv.org/pdf/2609.19779",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jct6afqcgm7c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19779",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19779"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system",
  "title_text": "Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/5jct6afqcgm7c",
  "venue": "arXiv",
  "versions": []
}