{
  "abstract": "This paper develops an explicit spectral-contraction approach to studying fully coupled nonlinear forward--backward stochastic difference equations on infinite horizon and their applications to stochastic control. The estimates for this fully coupled system are assembled into an explicit two-dimensional nonnegative matrix. Its spectral radius yields an explicit sufficient discount threshold, and a corresponding equivalent weighted product norm is constructed to establish the contraction property. Moreover, for an infinite-horizon control problem with convex control constraints and an accumulated discounted running cost, we derive a Pontryagin-type stochastic maximum principle, its equivalent pointwise normal-cone formulation, and a verification theorem. Finally, a recursive risk-adjusted portfolio example is given to demonstrate the applications of our theoretical results, and a projection-type sufficient optimality condition for this example is derived.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11354",
  "author_total": 2,
  "authors": [
    {
      "name": "Rui Chen"
    },
    {
      "name": "Qi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73jc2n69zxkq8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11354",
  "fulltext_url": null,
  "id": "73jc2n69zxkq8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11354",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.11354",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73jc2n69zxkq8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11354",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11354"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations: Spectral Contraction and Infinite-Horizon Maximum Principle",
  "title_text": "Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations: Spectral Contraction and Infinite-Horizon Maximum Principle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/73jc2n69zxkq8",
  "venue": "arXiv",
  "versions": []
}