In this paper, we propose a new efficient method for calculating the Gerber-Shiu discounted penalty function. Generally, the Gerber-Shiu function usually satisfies a class of integro-differential equation. We introduce the physics-informed neural networks (PINN) which embed a differential equation into the loss of the neural network using automatic differentiation. In addition, PINN is more free to set boundary conditions and does not rely on the determination of the initial value. This gives us an idea to calculate more general Gerber-Shiu functions. Numerical examples are provided to illustrate the very good performance of our approximation.

翻译：本文提出一种计算Gerber-Shiu贴现罚函数的高效新方法。通常，Gerber-Shiu函数满足一类积分-微分方程。我们引入物理信息神经网络（PINN），该方法通过自动微分将微分方程嵌入神经网络的损失函数中。此外，PINN可更灵活地设置边界条件，且不依赖初始值的确定。这为我们计算更广义的Gerber-Shiu函数提供了思路。数值算例表明，该近似方法具有极优性能。