Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Toshihiro Yamada: Graduate School of Economics, Hitotsubashi University and Japan Science and Technology Agenc

No CIRJE-F-1212, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expan- sion method with a deep learning-based algorithm. In particular, the mathematical justi cation on the spatial approximation is provided. Numerical examples for high-dimensional Kolmogorov PDEs show effectiveness of our method.

Pages: 28 pages
Date: 2023-04
New Economics Papers: this item is included in nep-big and nep-des
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2023cf1212

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