In this paper, we give a characterization of the optimal cost of an impulse control problem as the maximum solution of a quasi-variational inequality without assuming nondegeneracy. An estimate of the velocity of uniform convergence of the sequence of stopping time problems associated with the impulse control problem is given.
Numerical Analysis and Computation
J.-L. Menaldi, On the optimal impulse control problem for degenerate diffusions, SIAM J. Control Optim., 18 (1980), pp. 722-739. doi: 10.1137/0318053