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

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

doi:10.2139/ssrn.2598529

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2021

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“…In [70], 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 [71]. An approach that uses the associated FBSDE to train a neural network to learn the solution of a semilinear PDE is discussed in [146].…”

Section: Summary and Extensionsmentioning

confidence: 99%

Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review

Blechschmidt¹,

Ernst²

2021

Preprint

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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 the Deep BSDE solver. 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: Summary and Extensionsmentioning

confidence: 99%