$$\mathbb {L}^2$$ L 2 -solutions for reflected BSDEs with jumps under monotonicity and general growth conditions: a penalization method

Abstract

In this paper, we study generalized reflected backward stochastic differential equations with a cadlag barrier, in a general filtration that supports a Brownian motion and an independent Poisson random measure. We give necessary and sufficient conditions for existence and uniqueness of \(\mathbb {L}^2\)-solutions for equations with generators monotone in y. We also prove that the solutions can be approximated via the penalization method. Furthermore, a comparison theorem is provided for such equations.