A General Stochastic Maximum Principle For Optimal Control Of Stochastic Systems Driven By Multidimensional Teugel's Martingales

A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel’s martingales. The multidimensional Teugel’s martingales are constructed by orthogonalizing the multidimensional L'{e}vy processes. The control domain need not be convex, and the control is allowed to enter into the terms of Teugel’s martingales.