  We derive and analyze monotone difference-quadrature schemes for Bellman
equations of controlled Levy (jump-diffusion) processes. These equations are
fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of
viscosity solutions. We propose new ``direct'' discretizations of the non-local
part of the equation that give rise to monotone schemes capable of handling
singular Levy measures. Furthermore, we develop a new general theory for
deriving error estimates for approximate solutions of integro-PDEs, which
thereafter is applied to the proposed difference-quadrature schemes.
