Discussion Papers 2021
| CIRJE-F-1178 | "Deep Asymptotic Expansion: Application to Financial Mathematics" |
|---|---|
| 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 |
|---|
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 |