  We develop a novel deep learning approach for pricing European basket options
written on assets that follow jump-diffusion dynamics. The option pricing
problem is formulated as a partial integro-differential equation, which is
approximated via a new implicit-explicit minimizing movement time-stepping
approach, involving approximation by deep, residual-type Artificial Neural
Networks (ANNs) for each time step. The integral operator is discretized via
two different approaches: a) a sparse-grid Gauss--Hermite approximation
following localised coordinate axes arising from singular value decompositions,
and b) an ANN-based high-dimensional special-purpose quadrature rule.
Crucially, the proposed ANN is constructed to ensure the asymptotic behavior of
the solution for large values of the underlyings and also leads to consistent
outputs with respect to a priori known qualitative properties of the solution.
The performance and robustness with respect to the dimension of the methods are
assessed in a series of numerical experiments involving the Merton
jump-diffusion model.
