Please consider the following backward stochastic differential equation:
$$ Y(s)=\xi+\int\_{s}^{T}a(u)Y(u)+b(u)Y(u)Z(u)du-\int\_{s}^{T}Z(u)dW(u)$$
Here $a(s)$, $b(s)$ are square-integrable stochastic processes adapted to the standard filtration generated by the Brownian motion $W(s)$. $\xi$ is adapted to the whole Brownian path. 


**My question**: Is there any reference that discusses existence of a pair of solution $(Y,Z)$ to this BSDE?


Since Pardoux-Peng first paper on BSDEs which required Lipchitz's condition on the generator, many other mathematicians including Briand and Hu, Lepeltier and San Martin, Kobylanski, Bahlali, etc have attempted to weaken this hypothesis. Their hypothesis on the generator cover cases like linear growth in $y$,$z$; superlinear in $y$ and linear in $z$; superlinear in y and quadratic in $z$; logarithmic expression like $y \log\lvert y\rvert$, etc. None however has a term $yz$ in the generator. Closest I can find are the papers [here](https://arxiv.org/pdf/1402.6596.pdf) which treat generator $a+b\vert y\rvert+c \lvert z\rvert+f(y)\lvert z \rvert^2$ and [here](https://arxiv.org/abs/1810.05664), in which Bahlali consider the generator $\lvert z \rvert^2/y$.


Appreciate your insight to this problem. 



Is there solution to a backward stochastic differential equation with $yz$ in the generator?
An update: Khaled Bahlali has recently given sufficient conditions for one dimensional BSDE $(Y,Z)$ with generator containing $yz$ to have a solution. The paper is on Axriv [here](https://arxiv.org/abs/1903.11325).


