Discretisation of FBSDEs driven by càdlàg martingales

We study the discretisation of forward backward stochastic differential equations (FBSDEs) driven by càdlàg martingales. We prove that under certain conditions imposed on the parameters of the FBSDE the time-discrete scheme we consider converges to the time-continuous equation in the L2L2-sense. Moreover, we show that the L2L2-norm of the error is of the order of the time step.