Reflected Backward Doubly Stochastic Differential Equations Driven by Teugels Martingales Associated to a L\'evy Process with Discontinuous Barrier
2023, v.29, Issue 3, 329-346
In this paper, we present a generalization of reflected backward doubly stochastic
differential equations (RBDSDEs) driven by Teugels martingales associated to
a L\'evy process, with a lower not necessarily right continuous barrier. We prove existence and uniqueness of the solution using a fixed point argument.
Keywords: Reflected backward doubly stochastic differential equations; Teugels martingales; Mertens decomposition; Strong optional supermartingale