  We propose a deep learning algorithm for solving high-dimensional parabolic
integro-differential equations (PIDEs) and high-dimensional forward-backward
stochastic differential equations with jumps (FBSDEJs), where the
jump-diffusion process are derived by a Brownian motion and an independent
compensated Poisson random measure. In this novel algorithm, a pair of deep
neural networks for the approximations of the gradient and the integral kernel
is introduced in a crucial way based on deep FBSDE method. To derive the error
estimates for this deep learning algorithm, the convergence of Markovian
iteration, the error bound of Euler time discretization, and the simulation
error of deep learning algorithm are investigated. Two numerical examples are
provided to show the efficiency of this proposed algorithm.
