DNN expression rate analysis of high-dimensional PDEs: application to option pricing (Q2117328)

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English	DNN expression rate analysis of high-dimensional PDEs: application to option pricing	scientific article

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instance of

scholarly article

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title

DNN expression rate analysis of high-dimensional PDEs: application to option pricing (English)

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zbMATH Open document ID

1500.35009

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DOI

10.1007/s00365-021-09541-6

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Constructive Approximation

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publication date

21 March 2022

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full work available at URL

https://arxiv.org/abs/1809.07669

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Mathematics Subject Classification ID

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neural network approximation

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low-rank approximation

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option pricing

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high-dimensional PDEs

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describes a project that uses

DGM

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MaRDI profile type

MaRDI publication profile

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Universal approximation bounds for superpositions of a sigmoidal function

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Solving the Kolmogorov PDE by means of deep learning

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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

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Optimal Approximation with Sparsely Connected Deep Neural Networks

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Neural Networks for Localized Approximation

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Approximation by superpositions of a sigmoidal function

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Deep Neural Network Approximation Theory

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Functional Integration and Partial Differential Equations. (AM-109)

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Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs

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Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models

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Q5270493

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Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models

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Loss of regularity for Kolmogorov equations

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

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Solving parametric PDE problems with artificial neural networks

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Mathematical models of financial derivatives

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A machine learning framework for data driven acceleration of computations of differential equations

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

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Q4938227

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Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

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Nonparametric regression using deep neural networks with ReLU activation function

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Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

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DGM: a deep learning algorithm for solving partial differential equations

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Q5297902

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Error bounds for approximations with deep ReLU networks

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mardi Publication:2117328