  We study a discrete time approximation scheme for the solution of a doubly
reflected Backward Stochastic Differential Equation (DBBSDE in short) with
jumps, driven by a Brownian motion and an independent compensated Poisson
process. Moreover, we suppose that the obstacles are right continuous and left
limited (RCLL) processes with predictable and totally inaccessible jumps and
satisfy Mokobodski's condition. Our main contribution consists in the
construction of an implementable numerical sheme, based on two random binomial
trees and the penalization method, which is shown to converge to the solution
of the DBBSDE. Finally, we illustrate the theoretical results with some
numerical examples in the case of general jumps.
