The stochastic maximum principle for jump-diffusion optimal control problems of delay systems involving continuous and impulse controls and its applications to finance

This paper establishes a stochastic maximum principle for an optimal control of model which was drove by a Ito-Levy process with time delay involving continuous and impulse control. We also show the existence and uniqueness of the solution to a stochastic differential delay equation involving impulse control. As an application a kind of production and consumption choice optimization problem was solved.