Deep backward schemes for high-dimensional nonlinear PDEs
DOI10.1090/mcom/3514zbMath1440.60063arXiv1902.01599OpenAlexW2993551995WikidataQ114094322 ScholiaQ114094322MaRDI QIDQ4960067
Xavier Warin, Côme Huré, Huyên Pham
Publication date: 8 April 2020
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.01599
backward stochastic differential equationsoptimal stopping problemdeep neural networksnonlinear PDEs in high dimension
Probabilistic models, generic numerical methods in probability and statistics (65C20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)
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Cites Work
- Adapted solution of a backward stochastic differential equation
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Variational inequalities and the pricing of American options
- Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
- On irregular functionals of SDEs and the Euler scheme
- Reflected solutions of backward SDE's, and related obstacle problems for PDE's
- A numerical scheme for BSDEs
- Multilayer feedforward networks are universal approximators
- Nesting Monte Carlo for high-dimensional non-linear PDEs
- Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
- DGM: a deep learning algorithm for solving partial differential equations
- A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
- Convergence of the deep BSDE method for coupled FBSDEs
- On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
- Machine learning for semi linear PDEs
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
- Discrete-time approximation for continuously and discretely reflected BSDEs
- A regression-based Monte Carlo method to solve backward stochastic differential equations
- Error analysis of the optimal quantization algorithm for obstacle problems.
- Monte-Carlo Valuation of American Options: Facts and New Algorithms to Improve Existing Methods
- Solving high-dimensional partial differential equations using deep learning
- Deep optimal stopping
- Unnamed Item
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