# A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics

arXiv: https://arxiv.org/abs/2010.15757 · HTML: https://mlsanity.com/paper/2010.15757/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems](https://mlsanity.com/paper/2112.03749/) (2021)
- [Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics](https://mlsanity.com/paper/2109.11403/) (2021)
- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)

## Abstract (arXiv)

In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In this paper we propose a deep neural network algorithm for solving such partial differential equations in high dimensions. The algorithm is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with random terminal time.