  In this paper, we study multidimensional generalized BSDEs that have a
monotone generator in a general filtration supporting a Brownian motion and an
independent Poisson random measure. First, we prove the existence and
uniqueness of $\mathbb{L}^p(p\ge2)$-solutions in the case of a fixed terminal
time under suitable $p$-integrability conditions on the data. Then, we extend
these results to the case of a random terminal time. Furthermore, we provide a
comparison result in dimension $1$.
