ERROR ESTIMATES FOR APPROXIMATE SOLUTIONS TO BELLMAN EQUATIONS ASSOCIATED WITH CONTROLLED JUMP-DIFFUSIONS

摘要

We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jump-diffusion processes, which are fully nonlinear integro-partial differential equations. Two main results are obtained: (i) error bounds for a class of monotone approximation schemes, which includes finite difference schemes, and (ii) bounds on the error induced when the original Lévy measure is replaced by a finite measure with compact support, an apprximation process that is commonly used when designing numerical schemes for integro-partial differential equations. In our proofs we use and extend techniques introduced by Krylov and Barles-Jakobsen.