Contribution on the existence of solutions of coupled FBSDEs with monotone coefficients

Abstract

In this paper, we prove existence of a solution of a class of Forward Backward Stochastic Differential Equations (FBSDE) with Poisson random jumps  by weakening the usual Lipschitz conditions on the  generator of the backward equation with  jumps  and the drift of the forward equation with  jumps.   These coefficients are monotonic but can be discontinuous   and the diffusion term can be degenerated.