ABSTRACT
A necessary minimum principle is obtained for the optimal control of a semimartingale. The control is effected by changing the measure on the underlying space, which in turn varies the local characteristics of the process. A martingale representation result is not needed to represent the minimum cost process. Instead, this process is expressed as a stochastic integral plus an orthogonal martingale. The result generalizes previous work on the optimal control of Ito processes and jump processes.
