Solving high-dimensional partial differential equations using deep learning

Dynamic Programming (Princeton University Press, 1957)

Bellman, R. E · 1957

Earlier work this paper cites.

Option pricing and replication with transaction costs

Leland, H · 1985

Earlier work this paper cites.

Backward stochastic differential equations and quasilinear parabolic partial differential equations

Pardoux, É. & Peng, S · 1992

Earlier work this paper cites.

Option pricing with differential interest rates

Bergman, Y. Z · 1995

Earlier work this paper cites.

Pricing and hedging derivative securities in markets with uncertain volatilities

Avellaneda, M., Levy, A. & Parás, A · 1995

Earlier work this paper cites.

Recursive valuation of defaultable securities and the timing of resolution of uncertainty

Duffie, D., Schroder, M. & Skiadas, C · 1996

Earlier work this paper cites.

Backward stochastic differential equations in finance

El Karoui, N., Peng, S. & Quenez, M.-C · 1997

Earlier work this paper cites.

Approximation theory of the MLP model in neural networks

Pinkus, A · 1999

Earlier work this paper cites.

Forward-backward stochastic differential equations and quasilinear parabolic PDEs

Pardoux, É. & Tang, S · 1999

Earlier work this paper cites.

Stochastic Controls (Springer New York, 1999)

Yong, J. & Zhou, X · 1999

Earlier work this paper cites.

Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers

Forsyth, P. A. & Vetzal, K. R · 2001

Earlier work this paper cites.

The Diffuse Interface Approach in Materials Science: Thermodynamic Concepts and Applications of Phase-Field Models , vol. 73 (Springer Science & Business Media, 2003)

Emmerich, H · 2003

Cited alongside, same era.

The randomized information complexity of elliptic PDE

Heinrich, S · 2006

Cited alongside, same era.

Approximate Dynamic Programming: Solving the Curses of Dimensionality (John Wiley & Sons, 2011)

Powell, W. B · 2011

Cited alongside, same era.

Imagenet classification with deep convolutional neural networks

Krizhevsky, A., Sutskever, I. & Hinton, G. E · 2012

Cited alongside, same era.

Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups

Hinton, G. et al · 2012

Cited alongside, same era.

Counterparty risk valuation: a marked branching diffusion approach

Adam: a method for stochastic optimization

Kingma, D. & Ba, J · 2015

Later among the works it cites.

Batch normalization: Accelerating deep network training by reducing internal covariate shift

Ioffe, S. & Szegedy, C · 2015

Later among the works it cites.

Deep Learning (MIT Press, 2016)

Goodfellow, I., Bengio, Y. & Courville, A · 2016

Later among the works it cites.

Mastering the game of Go with deep neural networks and tree search

Silver, D., Huang, A., Maddison, C. J., Guez, A. et al · 2016

Later among the works it cites.

Algorithms for overcoming the curse of dimensionality for certain Hamilton–Jacobi equations arising in control theory and elsewhere

Darbon, J. & Osher, S · 2016

Later among the works it cites.

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations