MAXIMUM PRINCIPLES FOR OPTIMAL CONTROL OF FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS

We present various versions of the maximum principle for optimal control of forward- backward 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 Levy processes. We then present a Malliavin calculus approach which allows us to handle non-Markovian systems. Finally, we give examples of applications. [PUBLICATION ABSTRACT]