Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

Abstract

In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.

Penalization method for reflected BDSDEs with two-sided jumps and driven by Lévy process

“…For more developments on Reflected BSDEs when the barrier is not necessarily right-continuous, we refer to [1,6,16,19,23,25,26]. More recently, Marzougue and Sagna [27] extended the work of Berrhazi et al [8] to the case when the noise is driven also by an independent Poisson random measure under the so-called stochastic Lipschitz condition on the drivers.…”