{
  "abstract": "In this paper, motivated by discrete-time McKean-Vlasov optimal control problems with law-delay, a class of forward-backward stochastic difference equations is investigated. The main difficulties come from the absence of Ito's formula in the discrete-time setting, as well as the fully coupled structure in which the coefficients depend on both law-delayed and law-anticipated terms. Under suitable monotonicity conditions, the existence and uniqueness of solutions are established. Furthermore, a new monotonicity condition is introduced to address the associated optimal control problem. As an application, the unique optimal control for linear quadratic systems with law-delay is derived.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26424",
  "author_total": 1,
  "authors": [
    {
      "name": "Duocheng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bkn41kpzf8y4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26424",
  "fulltext_url": null,
  "id": "1bkn41kpzf8y4",
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  "landing_url": "https://arxiv.org/abs/2608.26424",
  "language": null,
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  "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.PR"
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    [
      "openalex",
      "2003|Stochastic processes and financial applications"
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  "openalex": "W7204528032",
  "pdf_url": "https://arxiv.org/pdf/2608.26424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bkn41kpzf8y4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2608.26424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26424"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay",
  "title_text": "Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1bkn41kpzf8y4",
  "venue": "arXiv",
  "versions": []
}