Discussion Papers 2021
CIRJE-F-1178 | "Deep Asymptotic Expansion: Application to Financial Mathematics" |
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Author Name | Iguchi, Yuga, Riu Naito, Yusuke Okano, Akihiko Takahashi and Toshihiro Yamada |
Date | November 2021 |
Full Paper | PDF file |
Remarks | Revised in February 2022. Published in Proceedings of IEEE CSDE 2021. |
Abstract |
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The paper proposes a new computational scheme for diffusion semigroups based on an asymptotic expansion with weak approximation and deep learning algorithm to solve high-dimensional Kolmogorov partial differential equations (PDEs). In particular, we give a spatial approximation for the solution of d-dimensional PDEs on a range [a, b] d without suffering from the curse of dimensionality. |
Keywords: Deep learning, Asymptotic expansion, Weak approximation, Kolmogorov PDEs, Malliavin calculus, Curse of dimensionality |