Considered are stochastic continuous-time control systems described by stochastic differential equations, which are defined by special martingals. Examples are given by the well known Ito equations with respect to a Wiener - or a Poisson process. By means of a performance index, regarding current yields as well as a terminal payment a control problem is formulated. The essential result in view of concrete evaluation is the approximation by a sequence of discrete-time finite dimensional control problems.