${\mathbb{L}}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients

Abstract

We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in ${\mathbb{L}}^p$ for $p\in (1,2]$. Our results apply to generators that are stochastic monotone in the $y$-variable, stochastic Lipschitz in the $z$-variable, and satisfy a general stochastic linear growth condition.