Year: 2026
Type: preprint
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 $α=β=1$.
Source: arXiv (Cornell University)
Author: Wang, Siyi
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7214340819