Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk
研究了深度参数化PDE方法中神经网络的逼近性质，首次给出双曲正切激活函数的深度神经网络具有维度无关收敛率的理论结果，并在金融行业的交易对手信用风险管理问题中验证了该方法在高维场景下的有效性。
Abstract The recently introduced deep parametric PDE method combines the efficiency of deep learning for high-dimensional problems with the reliability of classical PDE models. The accuracy of the deep parametric PDE method is determined by the best-approximation property of neural networks. We provide (to the best of our knowledge) the first approximation results, which feature a dimension-independent rate of convergence for deep neural networks with a hyperbolic tangent as the activation function. Numerical results confirm that the deep parametric PDE method performs well in high-dimensional settings by presenting in a risk management problem of high interest for the financial industry.