Reflected BSDE with rcll barrier driven by a process with jumps

The theory of backward stochastic differential equations (BSDEs) was developed by Pardoux and Peng [5]. El-Karoui et al. [1] have introduced the notion of one barrier reflected BSDE, which is a backward equation but the solution is forced to stay above a lower obstacle. Later Cvitanic and Karatzas [2] studied BSDEs with two reflecting barriers (DRBSDEs). And after, El Otmani [3] consider a reflected BSDE driven by a Brownian motion and the martingales of Teugels associated with a pure jump independent L�vy process and rcll obstacle. Recently, Marzougue and El Otmani [4] discussed the case of DRBSDE with the so-called stochastic Lipschitz coefficient. In this work, we study the reflected backward stochastic differential equations (RBSDEs) driven by a L�vy process and their applications in finance, in particular hedging of American option. We proved the existence an uniqueness of a solution to RBSDEs where the coefficient is stochastic Lipschitz by means of the penalization method.