Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics
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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.
Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 7 of its 34 references that are in the map. First posted on arXiv 23 Sep 2021.
Builds on
7 of 34 references.
References · 7
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
- 2017Solving high-dimensional partial differential equations using deep learningcited by 549
- 2019Deep splitting method for parabolic PDEscited by 53
- 2018Convergence of the Deep BSDE Method for Coupled FBSDEscited by 42
- 2016Mean Field Game of Controls and An Application To Trade Crowdingcited by 22
- 2019Neural networks-based backward scheme for fully nonlinear PDEscited by 21
- 2020A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematicscited by 3
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Citing papers per year: 2022: 2; 2023: 1; 2024: 2.
5 papers.
- 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
- 2022Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradientcited by 5
- 2023Temporal Difference Learning for High-Dimensional PIDEs with Jumpscited by 5
- 2022Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditionscited by 3
- 2024Multilevel 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-sensecited by 3
- 2024Multilevel 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-sense30 Sep 2024
- 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs8 May 2024
- 2023Temporal Difference Learning for High-Dimensional PIDEs with Jumps6 Jul 2023
- 2022Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient24 Oct 2022
- 2022Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions7 May 2022