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We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games.
Some machine learning schemes for high-dimensional nonlinear pdes
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Numerical analysis
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A regression-based monte carlo method to solve backward stochastic differential equations
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Numerical methods in finance and economics: a MATLAB-based introduction
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Stochastic Processes and Applications. Diffusions Processes, the Fokker-Planck and Langevin Equations
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Mean field games and systemic risk
Carmona, R., L.-H. Sun, and J.-P. Fouque (2015) · 2015
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Optimal execution with limit and market orders
Cartea, Á. and S. Jaimungal (2015) · 2015
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Algorithmic and high-frequency trading
Cartea, Á., S. Jaimungal, and J. Penalva (2015) · 2015
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Mean field game of controls and an application to trade crowding
Cardaliaguet, P. and C.-A. Lehalle (2017) · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
E, W., J. Han, and A. Jentzen (2017) · 2017
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On the policy improvement algorithm in continuous time
Jacka, S. D. and A. Mijatocíc (2017) · 2017
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Solving nonlinear and high-dimensional partial differential equations via deep learning
Al-Aradi, A., A. Correia, D. Naiff, G. Jardim, and Y. Saporito (2018) · 2018
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Solving high-dimensional partial differential equations using deep learning
Han, J., A. Jentzen, and W. E (2018) · 2018
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Srivastava, R. K., K. Greff, and J. Schmidhuber (2015) · 2015
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Incorporating order-flow into optimal execution
Cartea, Á. and S. Jaimungal (2016) · 2016
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Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
E, W., M. Hutzenthaler, A. Jentzen, and T. Kruse (2016) · 2016
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DGM: A deep learning algorithm for solving partial differential equations
Sirignano, J. and K. Spiliopoulos (2018) · 2018
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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
Hutzenthaler, M., A. Jentzen, T. Kruse, and T. A. Nguyen (2019) · 2019
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Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
Hutzenthaler, M., A. Jentzen, and P. von Wurstemberger (2019) · 2019
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