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

TL;DR

This paper proves the existence and uniqueness of solutions in ^p for multidimensional generalized backward stochastic differential equations with stochastic monotone coefficients in a general filtration, broadening the scope of solvable GBSDEs.

Contribution

It introduces new ^p solutions for GBSDEs with stochastic monotone generators under weak assumptions in a general filtration.

Findings

Established ^p existence and uniqueness for GBSDEs

Applicable to generators with stochastic monotonicity and Lipschitz conditions

Extended solvability to a broad class of GBSDEs in general filtrations

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.