Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps

Abstract. We present various versions of the maximum principle for optimal control of forwardbackward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Lévy processes. We then present a Malliavin calculus approach which allows us to handle non–Markovian systems. Finally, we give examples of applications.