  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.

Numerical Analysis;Numerical Analysis;Probability;Risk Management