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Generic well-posedness for a family of quadratic BSDE systems — arXiv:2609.29762

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29762
License (as archived): CC0-1.0
Archived: 2026-10-08T06:07:51.649Z
SHA-256 of the archived text: 799ac82ffae28823e0e1750e23fe8d41728bc28c4a25c9c6205fd8e0c9dedb7c
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Generic well-posedness for a family of quadratic BSDE systems — arXiv:2609.29762 — arXiv (en), https://arxiv.org/abs/2609.29762 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8a47ded68eec (Metraipolis archive dc_8a47ded68eec, sha256 799ac82ffae28823e0e1750e23fe8d41728bc28c4a25c9c6205fd8e0c9dedb7c)

BibTeX

@misc{dc8a47ded68eec,
  title = {Generic well-posedness for a family of quadratic BSDE systems — arXiv:2609.29762},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29762},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8a47ded68eec; sha256 799ac82ffae28823e0e1750e23fe8d41728bc28c4a25c9c6205fd8e0c9dedb7c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29762. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $1/\alpha+1/\beta=1$. For every $\alpha,\beta>0$ and $M>0$, we establish existence and uniqueness in $\mathcal{S}^{\infty}\times\mathrm{BMO}$ for a dense $G_\delta$ subset of the space of terminal data satisfying $|\xi_i|\le M$ 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 $1/\alpha+1/\beta\ne1$, 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 $\alpha=\beta=1$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.29762 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T05:35:05.146Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).