A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA

Henry-Labordère, Pierre; Litterer, Christian; Ren, Zhenjie

doi:10.1137/15m1019945

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Semilinear Pdes In High Dimensions1

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2023

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Cited by 6 publications

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“…In [71], an extension based on a primal‐dual solution method for BSDEs using neural networks and a dual formulation of stochastic control problems is discussed, see also [72]. An approach that uses the associated FBSDE to train a neural network to learn the solution of a semilinear PDE is discussed in [152].…”

Section: Semilinear Pdes In High Dimensionsmentioning

confidence: 99%

Three ways to solve partial differential equations with neural networks — A review

2021

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Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high‐dimensional problems: physics‐informed neural networks, methods based on the Feynman–Kac formula and methods based on the solution of backward stochastic differential equations. The article is accompanied by a suite of expository software in the form of Jupyter notebooks in which each basic methodology is explained step by step, allowing for a quick assimilation and experimentation. An extensive bibliography summarizes the state of the art.

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Section: Semilinear Pdes In High Dimensionsmentioning

confidence: 99%