A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equation

Maxim Bichuch; Ke Chen

doi:10.1142/9789811280306_0004

A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equation

Maxim Bichuch
, Ke Chen

Mathematics

Johns Hopkins University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

We study the convergence of a deep learning algorithm applied to a general class of fully nonlinear second-order partial differential equations. By using a suitable finite difference approximation to the loss function of the deep learning scheme, we show the convergence of the numerical solution to the unique viscosity solution. We apply our results and illustrate this convergence to the finite horizon optimal investment problem with proportional transaction costs in single and multi-asset settings.

Original language	English
Title of host publication	Peter Carr Gedenkschrift
Subtitle of host publication	Research Advances in Mathematical Finance
Publisher	World Scientific Publishing Co.
Pages	101-140
Number of pages	40
ISBN (Electronic)	9789811280306
ISBN (Print)	9789811280290
DOIs	https://doi.org/10.1142/9789811280306_0004
State	Published - Jan 1 2023

Keywords

Convergence
Deep learning
Machine learning
Optimal investment
Partial differential equation
Transaction costs

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10.1142/9789811280306_0004

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KW - Optimal investment

KW - Partial differential equation

KW - Transaction costs

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A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equation

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Keywords

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