Necessary and sufficient conditions for optimal control of stochastic systems associated with Lévy processes.

The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel’s martingales and an independent multi-dimensional Brownian motion. Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation, and the coefficients appearing in the systems are allowed to depend on the control variables. As an application, the linear quadratic stochastic optimal control problem is studied. [ABSTRACT FROM AUTHOR]