Path-Dependent Deep Galerkin Method: A Neural Network Approach to Solve Path-Dependent Partial Differential Equations

DOI10.1137/20M1329597zbMath1471.91621arXiv2003.02035OpenAlexW3190588512WikidataQ115246900 ScholiaQ115246900MaRDI QIDQ4958400

Yuri F. Saporito, Zhaoyu Zhang

Publication date: 8 September 2021

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.02035

zbMATH Keywords

neural networksfunctional Itô calculuslong short-term memorypath-dependent partial differential equationsdeep Galerkin method

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (2)

A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations ⋮ Deep signature FBSDE algorithm

Uses Software

• DGM

Cites Work

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• Viscosity solutions of fully nonlinear parabolic path dependent PDEs. I.
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs. II
• An infinite-dimensional approach to path-dependent Kolmogorov equations
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Change of variable formulas for non-anticipative functionals on path space
• Functional Itô calculus, path-dependence and the computation of Greeks
• DGM: a deep learning algorithm for solving partial differential equations
• A martingale approach for fractional Brownian motions and related path dependent PDEs
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• On the convergence of monotone schemes for path-dependent PDEs
• On viscosity solutions of path dependent PDEs
• Neural algorithm for solving differential equations
• The functional Itō formula under the family of continuous semimartingale measures
• Two Person Zero-Sum Game in Weak Formulation and Path Dependent Bellman--Isaacs Equation
• Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
• Advanced Monte Carlo Methods for Barrier and Related Exotic Options
• Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost
• Solving high-dimensional partial differential equations using deep learning
• Functional Itô calculus

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