Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk

TL;DR

This paper introduces a boundary-safe PINNs extension for solving non-linear parabolic PDEs in counterparty credit risk, improving boundary condition handling and leveraging automatic differentiation for accurate derivatives.

Contribution

A novel boundary condition treatment in PINNs that eliminates heuristic weight tuning, enhancing PDE solution accuracy in financial risk modeling.

Findings

Effective boundary condition handling without heuristic weights

Improved accuracy in non-linear PDE solutions

Potential for broader application in financial modeling

Abstract

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.