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.

翻译：我们提出了一种新颖的深度学习方法，用于定价遵循跳扩散动态的资产欧式篮子期权。期权定价问题被表述为一个偏积分微分方程，通过一种新的隐式-显式最小化移动时间步进方法进行近似，该方法在每个时间步采用深度残差型人工神经网络进行逼近。积分算子的离散化通过两种不同方式实现：(a) 基于奇异值分解得到的局部坐标轴，采用稀疏网格高斯-埃尔米特近似；(b) 一种基于人工神经网络的高维专用求积规则。关键之处在于，所提出的人工神经网络被设计为确保解在标的资产较大值时的渐近行为，并使得输出与先验已知的解的定性性质保持一致。通过一系列涉及默顿跳扩散模型的数值实验，评估了该方法在高维情况下的性能与稳健性。