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We consider a fully coupled forward backward stochastic differential equation driven by a Lévy processes having moments of all orders and an independent Brownian motion. Under some monotonicity assumptions, we prove the existence and uniqueness of solutions on an arbitrarily fixed large time duration. We use this result to prove the existence of an open-loop Nash equilibrium point for non-zero sum stochastic differential games.

Fully coupled forward backward stochastic differential equations driven by Lévy processes and application to differential games