A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics
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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.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2020.
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Citing papers per year: 2021: 2; 2022: 0; 2023: 0; 2024: 1.
3 papers.
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problemscited by 21
- 2021Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematicscited by 5
- 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equationscited by 4
- 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations12 Apr 2024
- 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems7 Dec 2021
- 2021Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics23 Sep 2021