  High-dimensional parabolic partial integro-differential equations (PIDEs)
appear in many applications in insurance and finance. Existing numerical
methods suffer from the curse of dimensionality or provide solutions only for a
given space-time point. This gave rise to a growing literature on deep learning
based methods for solving partial differential equations; results for
integro-differential equations on the other hand are scarce. In this paper we
consider an extension of the deep splitting scheme due to Beck, Becker,
Cheridito, Jentzen, Neufeld (2021) and Germain, Pham, Warin (2022) to PIDEs.
Our main contribution is a convergence analysis of the scheme. Moreover we
discuss several test case studies to show the viability of our approach.
