Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics

TL;DR

This paper develops deep neural network algorithms to solve high-dimensional linear and semilinear parabolic partial integro-differential equations, demonstrating their effectiveness through case studies in insurance and finance.

Contribution

It introduces novel deep learning methods tailored for solving complex integro-differential equations in high dimensions, an area with limited prior research.

Findings

Successful application to insurance mathematics problems

Effective handling of high-dimensional equations

Potential for broad application in finance and insurance

Abstract

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.