On the Impulse Control of Jump Diffusions

Regularity of the impulse control problem for a nondegenerate n-dimensional jump diffusion with infinite activity and finite variation jumps was recently examined in [M. H. A. Davis, X. Guo, and G. Wu, SIAM J. Control Optim., 48 (2010), pp. 5276--5293]. Here we extend the analysis to include infinite activity and infinite variation jumps. More specifically, we show that the value function u of the impulse control problem satisfies u∈ W2,ploc(Rⁿ).