Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus (Forthcoming in "Partial Differential Equations and Applications")(Revised version of CARF-F-547)

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: The University of Tokyo
Toshihiro Yamada: Hitotsubashi University, Japan Science and Technology Agency (JST)

No CARF-F-560, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The 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 expansion method with a deep learning-based algorithm. In particular, the mathematical justification on the spatial approximation is provided. Numerical examples for high-dimensional Kolmogorov PDEs show effectiveness of our method.

Pages: 28
Date: 2023-05
New Economics Papers: this item is included in nep-big and nep-des
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