Optimal Control of Forward-Backward Stochastic Differential System of Jump Diffusion with Observation Noise: Stochastic Maximum Principle

This paper is concerned with the partial information optimal control problem of wa controlled forward-backward stochastic differential equation of jump diffusion with correlated noises between the system and the observation. For this type of partial information optimal control problem, Necessary and sufficient optimality conditions, in the form of Pontryagin maximum principle, for the partial information optimal control are established using a unified way. Moreover, our admissible control process $u(\cdot )$ satisfies the following integrable condition condition: \begin{equation*} \label{eq:1.16} \mathbb E\bigg[\int_0^T|u(t)|^4 dt\bigg]<\infty, \end{equation*}