Deep high-order splitting method for semilinear degenerate PDEs and application to high-dimensional nonlinear pricing models

Riu Naito () and Toshihiro Yamada ()
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Riu Naito: Hitotsubashi University & Japan Post Insurance Co., Ltd.
Toshihiro Yamada: Hitotsubashi University

Digital Finance, 2024, vol. 6, issue 4, No 4, 693-725

Abstract: Abstract The paper introduces a new deep learning-based high-order discretization method for semilinear degenerate parabolic partial differential equations based on a Gaussian Kusuoka approximation and shows its application to finance. The proposed deep learning-based algorithm for solving high-dimensional nonlinear problems is efficiently implemented without suffering from the curse of dimensionality. We show numerical examples for high-dimensional (100- and 150-dimensional) nonlinear pricing models and check the effectiveness of the proposed method.

Keywords: Semilinear PDEs; Deep learning; Gaussian Kusuoka approximation; High-dimensional financial diffusions; CVA (search for similar items in EconPapers)
JEL-codes: C45 C63 G13 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42521-023-00091-z

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