  General theorems for existence and uniqueness of viscosity solutions for
Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral
term are established. Such nonlinear partial integro-differential equations
(PIDE) arise in the study of combined impulse and stochastic control for
jump-diffusion processes. The HJBQVI consists of an HJB part (for stochastic
control) combined with a nonlocal impulse intervention term.
  Existence results are proved via stochastic means, whereas our uniqueness
(comparison) results adapt techniques from viscosity solution theory. This
paper is to our knowledge the first treating rigorously impulse control for
jump-diffusion processes in a general viscosity solution framework; the jump
part may have infinite activity. In the proofs, no prior continuity of the
value function is assumed, quadratic costs are allowed, and elliptic and
parabolic results are presented for solutions possibly unbounded at infinity.
