Deep Asymptotic Expansion: Application to Financial Mathematics
- Resource Type
- Conference
- Authors
- Iguchi, Yuga; Naito, Riu; Okano, Yusuke; Takahashi, Akihiko; Yamada, Toshihiro
- Source
- 2021 IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE) Computer Science and Data Engineering (CSDE), 2021 IEEE Asia-Pacific Conference on. :1-6 Dec, 2021
- Subject
- Bioengineering
Communication, Networking and Broadcast Technologies
Computing and Processing
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Deep learning
Computer science
Handheld computers
Partial differential equations
Conferences
Approximation algorithms
Hypercubes
Asymptotic expansion
Weak approximation
Kolmogorov PDEs
Malliavin calculus
Curse of dimensionality
- Language
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.