A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation

Riu Naito, Toshihiro Yamada
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Abstract

The paper introduces a deep learning-based high-order operator splitting method for nonlinear parabolic partial differential equations (PDEs) by using a Malliavin calculus approach. Through the method, a solution of a nonlinear PDE is accurately approximated even when the dimension of the PDE is high. As an application, the method is applied to the CVA computation in high-dimensional finance models. Numerical experiments performed on GPUs show the efficiency of the proposed method.
基于Malliavin演算的高维非线性抛物型偏微分方程的深度学习高阶算子分裂方法:在CVA计算中的应用
介绍了一种基于深度学习的非线性抛物型偏微分方程的高阶算子分裂方法。通过该方法,即使非线性偏微分方程的维数很高,也能精确地逼近解。将该方法应用于高维金融模型的CVA计算。在图形处理器上进行的数值实验表明了该方法的有效性。
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