论文标题
边界安全PINNS扩展：在交易对手信用风险中应用于非线性抛物线PDE
Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk
论文作者
论文摘要
这项工作的目的是开发深度学习数值方法来解决非线性PDE模型给出的XVA定价问题。提出了一种新的边界条件处理策略，它可以摆脱与训练过程相关的损失函数中出现的不同加成的权重选择。它基于通过将相关条件替换为模型方程本身而产生的PDE来定义与边界相关的损失。此外，采用自动分化来获得部分衍生物的准确近似。
The goal of this work is to develop deep learning numerical methods for solving option XVA pricing problems given by non-linear PDE models. A novel strategy for the treatment of the boundary conditions is proposed, which allows to get rid of the heuristic choice of the weights for the different addends that appear in the loss function related to the training process. It is based on defining the losses associated to the boundaries by means of the PDEs that arise from substituting the related conditions into the model equation itself. Further, automatic differentiation is employed to obtain accurate approximation of the partial derivatives.
