用自适应神经网络求解多资产期权定价，精度高且稳定。
Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems
- 基于径向基函数网络构建物理信息模型，自动优化网络结构。
- 在非光滑收益条件下仍保持高精度，四资产期权误差低于0.5%。
- 适合金融工程中复杂衍生品定价，尤其适用于高维问题。
本文研究多资产期权定价的Black-Scholes偏微分方程（PDE）数值解法。提出一种基于径向基函数神经网络（RBFNN）的物理信息机器学习算法（PIRBFNN），同时优化网络结构并预测期权价格。该方法融合传统径向基函数配置法与物理信息神经网络优势，通过基于PDE残差的自适应策略动态调整隐藏神经元分布，在训练过程中提升求解效率。该方法有效处理具有非光滑收益条件的高维期权定价模型。实验验证涵盖单资产欧式看跌期权、双资产互换期权及四资产篮子看涨期权，结果表明其具备高精度与强鲁棒性。
原文摘要 · Abstract (English)
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.
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