A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Citations

Cited by:

1. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2021. "Deep Learning Algorithms for Hedging with Frictions," Papers 2111.01931, arXiv.org, revised Dec 2022.
2. Philipp Grohs & Arnulf Jentzen & Diyora Salimova, 2022. "Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms," Partial Differential Equations and Applications, Springer, vol. 3(4), pages 1-41, August.
3. Aur'elien Alfonsi & Adel Cherchali & Jose Arturo Infante Acevedo, 2020. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Papers 2010.12651, arXiv.org, revised Apr 2021.
4. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
5. Nikolas Nüsken & Lorenz Richter, 2021. "Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-48, August.
6. Ashley Davey & Harry Zheng, 2020. "Deep Learning for Constrained Utility Maximisation," Papers 2008.11757, arXiv.org, revised Aug 2021.
7. Christian Beck & Lukas Gonon & Arnulf Jentzen, 2024. "Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations," Partial Differential Equations and Applications, Springer, vol. 5(6), pages 1-47, December.
8. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
9. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
10. Marlon Azinovic & Luca Gaegauf & Simon Scheidegger, 2022. "Deep Equilibrium Nets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1471-1525, November.
11. Lukas Gonon, 2024. "Deep neural network expressivity for optimal stopping problems," Finance and Stochastics, Springer, vol. 28(3), pages 865-910, July.
12. Alfonsi, Aurélien & Cherchali, Adel & Infante Acevedo, Jose Arturo, 2021. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 234-260.
13. Chen, Yu & Yu, Hui & Liu, Chengjie & Xie, Jin & Han, Jun & Dai, Houde, 2024. "Synergistic fusion of physical modeling and data-driven approaches for parameter inference to enzymatic biodiesel production system," Applied Energy, Elsevier, vol. 373(C).
14. Marc Sabate-Vidales & David v{S}iv{s}ka & Lukasz Szpruch, 2020. "Solving path dependent PDEs with LSTM networks and path signatures," Papers 2011.10630, arXiv.org.
15. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.
16. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential L\'evy models," Papers 2101.11897, arXiv.org, revised Jul 2021.
17. Aur'elien Alfonsi & Bernard Lapeyre & J'er^ome Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Papers 2209.04153, arXiv.org, revised May 2023.
18. Kathrin Glau & Linus Wunderlich, 2020. "The Deep Parametric PDE Method: Application to Option Pricing," Papers 2012.06211, arXiv.org.
19. Stefan Kremsner & Alexander Steinicke & Michaela Szolgyenyi, 2020. "A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics," Papers 2010.15757, arXiv.org, revised Dec 2020.
20. Ariel Neufeld & Philipp Schmocker & Sizhou Wu, 2024. "Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs," Papers 2405.05192, arXiv.org, revised Jan 2025.
21. Lukas Gonon, 2021. "Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality," Papers 2106.08900, arXiv.org.
22. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Post-Print hal-03770051, HAL.
23. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.
24. Marc Sabate Vidales & David Siska & Lukasz Szpruch, 2018. "Unbiased deep solvers for linear parametric PDEs," Papers 1810.05094, arXiv.org, revised Jan 2022.
25. Ashley Davey & Michael Monoyios & Harry Zheng, 2020. "Duality for optimal consumption with randomly terminating income," Papers 2011.00732, arXiv.org, revised May 2021.
26. Ashley Davey & Harry Zheng, 2022. "Deep Learning for Constrained Utility Maximisation," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 661-692, June.
27. Jorino van Rhijn & Cornelis W. Oosterlee & Lech A. Grzelak & Shuaiqiang Liu, 2021. "Monte Carlo Simulation of SDEs using GANs," Papers 2104.01437, arXiv.org.
28. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Working Papers hal-03770051, HAL.