A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward‐backward systems

We consider a combined stochastic control and impulse control problem of forward-backward systems driven by Levy processes, where both the system coefficients and the objective performance functional are allowed to be random, non-Markovian; the information available to the controller is partial information. Applying a Malliavin calculus approach, we derive a maximum principle for this control problem, where the adjoint processes are explicitly represented by the parameters and the states of the system. Finally, we give two examples of applications. © 2015 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd