A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations

From MaRDI portal
Publication:5889064

DOI10.1090/memo/1410OpenAlexW2890889625MaRDI QIDQ5889064

Philippe von Wurstemberger, Fabian Hornung, Arnulf Jentzen, Philipp Grohs

Publication date: 26 April 2023

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02362




Related Items (16)

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation dataAn efficient Monte Carlo scheme for Zakai equationsMonte Carlo simulation of SDEs using GANsSolving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemesA Kolmogorov-Chentsov type theorem on general metric spaces with applications to limit theorems for Banach-valued processesNumerical methods for backward stochastic differential equations: a surveySolving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculusHow many inner simulations to compute conditional expectations with least-square Monte Carlo?Applications of artificial neural networks to simulating Lévy processesAn overview on deep learning-based approximation methods for partial differential equationsPhysics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled dataModeling the dynamics of PDE systems with physics-constrained deep auto-regressive networksOn existence and uniqueness properties for solutions of stochastic fixed point equationsDeep Splitting Method for Parabolic PDEsVariational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equationsMachine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations


Uses Software


Cites Work


This page was built for publication: A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations