{
  "abstract": "We study a two-parameter family of quadratic BSDE systems of the form given by Jackson (2023) in his open questions on non-Markovian solvability. Fan, Hu, and Tang (2025) established well-posedness for every bounded terminal datum when $1/α+1/β=1$. For every $α,β>0$ and $M>0$, we establish existence and uniqueness in $\\mathcal{S}^{\\infty}\\times\\mathrm{BMO}$ for a dense $G_δ$ subset of the space of terminal data satisfying $|ξ_i|\\le M$ a.s., $i=1,2$, equipped with the topology of convergence in probability. We also obtain well-posedness for every terminal datum taking at most two values. Furthermore, we show that every bounded terminal problem can be reduced to one with a three-valued terminal datum while preserving its solution set. However, for every positive parameter pair with $1/α+1/β\\ne1$, we construct a three-valued terminal datum admitting at least two distinct solutions in $\\mathcal{S}^{\\infty}\\times\\mathrm{BMO}$. In particular, uniqueness can fail in Jackson's stochastic-game example $α=β=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29762",
  "author_total": 1,
  "authors": [
    {
      "name": "Siyi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qqzetcy3zyad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29762",
  "fulltext_url": null,
  "id": "6qqzetcy3zyad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29762",
  "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.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7214340819",
  "pdf_url": "https://arxiv.org/pdf/2609.29762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qqzetcy3zyad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.29762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Generic well-posedness for a family of quadratic BSDE systems",
  "title_text": "Generic well-posedness for a family of quadratic BSDE systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6qqzetcy3zyad",
  "venue": "arXiv",
  "versions": []
}