Abstract: I will discuss comparison and continuous dependence results for the Hamilton–Jacobi–Bellman integro-PDE and applications to regularity, a priori estimation, and error estimation for approximation schemes. The equation is a non-linear integro-PDE arising in optimal control of jump-diffusion processes. Such equations have been used in financial models, eg, in the portfolio selection problem in a jump-diffusion stock marked. Models like this have been considered by Tourin, Barles, Pham, Karlsen, Øksendal and others. This is joint work with Kenneth Karlsen (Bergen/Oslo).