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

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

7 September 2018

Philippe von Wurstemberger

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

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Title
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations Jiequn Han Arnulf Jentzen Weinan E AI4CE 68 1 0 07 May 2025
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 97 7 0 08 May 2024
Computing excited states of molecules using normalizing flows Yahya Saleh Álvaro Fernández Corral Emil Vogt Armin Iske J. Küpper A. Yachmenev 84 7 0 31 Aug 2023
Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems C. Reisinger Yufei Zhang 53 70 0 15 Mar 2019
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 73 95 0 01 Jun 2018
Universal approximations of invariant maps by neural networks Dmitry Yarotsky 126 213 0 26 Apr 2018
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations M. Raissi 114 188 0 19 Apr 2018
Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm David Silver Thomas Hubert Julian Schrittwieser Ioannis Antonoglou Matthew Lai ... D. Kumaran T. Graepel Timothy Lillicrap Karen Simonyan Demis Hassabis 164 1,785 0 05 Dec 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 130 1,393 0 30 Sep 2017
Optimal Approximation with Sparsely Connected Deep Neural Networks Helmut Bölcskei Philipp Grohs Gitta Kutyniok P. Petersen 202 256 0 04 May 2017
The Power of Depth for Feedforward Neural Networks Ronen Eldan Ohad Shamir 230 732 0 12 Dec 2015
Provable approximation properties for deep neural networks Uri Shaham A. Cloninger Ronald R. Coifman 188 231 0 24 Sep 2015
Speech Recognition with Deep Recurrent Neural Networks Alex Graves Abdel-rahman Mohamed Geoffrey E. Hinton 232 8,529 0 22 Mar 2013