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This paper is concerned with necessary and sufficient optimality conditions for optimal control of jump-diffusion stochastic differential equations. Compared with the existing literature, there are two distinguishing features: one is that the states are driven by Brownian motions and Poisson random measure; the other one is that the states and the observations are correlated. We derive a necessary and a sufficient conditions in the form of maximum principle when control domain is convex. A linear-quadratic example is worked out to illustrate the applications of the foregoing optimality conditions.

Optimality Conditions for Optimal Control of Jump-Diffusion SDEs with Correlated Observations Noises