Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12704 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911384101453824 |
|---|---|
| author | Ma, Yan Ren, Yumeng |
| author_facet | Ma, Yan Ren, Yumeng |
| contents | The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems Ma, Yan Ren, Yumeng Machine Learning The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option. |
| title | Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.12704 |