Infinite horizon impulse control of stochastic functional differential equations driven by Levy processes

We consider impulse control of stochastic functional differential equations (SFDEs) driven by Levy processes under an additional L-p-Lipschitz condition on the coefficients. Our results, which are first derived for a general stochastic optimization problem over infinite horizon impulse controls and then applied to the case of a controlled SFDE, apply to the infinite horizon as well as the random horizon settings. The methodology employed to show existence of optimal controls is a probabilistic one based on the concept of Snell envelopes.