On finite difference schemes for partial integro-differential equations of Levy type

摘要

In this article we introduce a finite difference approximation for integro-differential operators of Levy type. We approximate solutions of possibly degenerate integro-differential equations by treating the nonlocal operator as a second-order operator on the whole unit ball, eliminating the need for truncation of the Levy measure which is present in the existing literature. This yields an approximation scheme with significantly reduced computational cost, especially for Levy measures corresponding to processes with jumps of infinite variation. Crown Copyright (C) 2019 Published by Elsevier B.V. All rights reserved.