Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics
This addresses a gap in applying deep learning to integro-differential equations, which is incremental but relevant for insurance and finance practitioners.
The paper tackles the numerical solution of high-dimensional parabolic partial integro-differential equations (PIDEs) using deep neural network algorithms, demonstrating viability through case studies in insurance and finance.
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep neural network algorithms for solving linear and semilinear parabolic partial integro-differential equations with boundary conditions in high dimension. To show the viability of our approach we discuss several case studies from insurance and finance.