{
  "abstract": "We study a new class of mean-field quadratic backward stochastic differential equations (qBSDEs) arising from mean-field portfolio games with exponential utility. Typical examples of such games include a mean-field portfolio game with price impact, and a finite-contract pricing model with market clearing conditions. Generators of these mean-field qBSDEs contain quadratic terms $\\mathbb{E}[Z]^{\\top} Z$ and $|\\mathbb{E}[Z]|^2$, instead of the classical pathwise $Z^\\top Z$ term. We prove local well-posedness under $L^q$-integrability assumptions on terminals and their Malliavin derivatives, and global well-posedness under an extra exponential integrability condition on the Malliavin derivatives. Then we show the existence and uniqueness of global equilibria of the above two mean-field games via our qBSDE theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07909",
  "author_total": 1,
  "authors": [
    {
      "name": "Huilin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feanmv8760vyn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07909",
  "fulltext_url": null,
  "id": "feanmv8760vyn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07909",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7212032222",
  "pdf_url": "https://arxiv.org/pdf/2609.07909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feanmv8760vyn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Mean-field quadratic BSDEs and related mean-field portfolio games of controls",
  "title_text": "Mean-field quadratic BSDEs and related mean-field portfolio games of controls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/feanmv8760vyn",
  "venue": "arXiv",
  "versions": []
}