Sammendrag
We find a maximum principle for processes driven by martingale random fields. We do so by describing the adjoint processes with non-anticipating stochastic derivatives. In the case of the Levy processes this mimics maximum principles with Malliavin derivatives, but we replace Malliavin differentiability conditions with L2-conditions. As an application we use the maximum principle to solve a portfolio optimization problem for assets with credit risk modeled by doubly stochastic Poisson processes.