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 ∈ Wloc2,p(Rn).
Numerical Analysis and Computation
E. Bayraktar, T. Emmerling and J.-L. Menaldi, On the impulse control of jump diffusions, SIAM J. Control Optim., 51 (2013), pp. 2612-2637. doi: 10.1137/120863836