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

arXiv: https://arxiv.org/abs/2109.11403 · HTML: https://mlsanity.com/paper/2109.11403/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 23 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep splitting method for parabolic PDEs](https://mlsanity.com/paper/1907.03452/) (2019)
- [Convergence of the Deep BSDE Method for Coupled FBSDEs](https://mlsanity.com/paper/1811.01165/) (2018)
- [Mean Field Game of Controls and An Application To Trade Crowding](https://mlsanity.com/paper/1610.09904/) (2016)
- [Neural networks-based backward scheme for fully nonlinear PDEs](https://mlsanity.com/paper/1908.00412/) (2019)
- [A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics](https://mlsanity.com/paper/2010.15757/) (2020)

## Built on by (most cited first, 5 of 5)

- [Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs](https://mlsanity.com/paper/2405.05192/) (2024)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)
- [Temporal Difference Learning for High-Dimensional PIDEs with Jumps](https://mlsanity.com/paper/2307.02766/) (2023)
- [Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions](https://mlsanity.com/paper/2205.03672/) (2022)
- [Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sense](https://mlsanity.com/paper/2409.20431/) (2024)

## Abstract (arXiv)

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.