${\mathbb{L}}^p$-solutions $(1<p<2)$ for reflected BSDEs with general jumps and stochastic monotone generators

Abstract

We consider a one-reflected backward stochastic differential equation with a general RCLL barrier in a filtration that supports a Brownian motion and an independent Poisson random measure. We establish the existence and uniqueness of a solution in ${\mathbb{L}}^p$ for $p\in (1,2)$. The result is obtained by means of the penalization method, under the assumption that the coefficient is stochastically monotone with respect to the state variable $y$, stochastically Lipschitz with respect to the control variables $(z,u)$, and satisfies suitable linear growth and $p$-integrability conditions.