On RBSDELs with time-delayed generators and RCLL obstacle

Abstract This paper delves into an in-depth analysis of the solution to a Reflected Backward Stochastic Differential Equation driven by a homogeneous Lévy process (RBSDEL in short) and characterized by a time-delayed generator, along with a lower obstacle Right Continuous Left-hand Limited (RCLL in short). Within our study, we present an a priori estimate and establish the existence and uniqueness of this solution using article [M. El Jamali and M. El Otmani, BSDE with rcll reflecting barrier driven by a Lévy process, Random Oper. Stoch. Equ. 28 2020, 1, 63–77] and the fixed-point theorem.