Generalized backward stochastic differential equations with jumps in a general filtration

Abstract

Abstract In this paper, we analyze multidimensional generalized backward stochastic differential equations with jumps in a filtration that supports a Brownian motion and an independent integer-valued random measure. Under monotonicity and linear growth assumptions on the coefficients, we give the existence and uniqueness of 𝕃 2 {\mathbb{L}^{2}} -solutions provided that the generators and the terminal condition satisfy some suitable integrability conditions.