Annals of Applied Probability

A monotone scheme for high-dimensional fully nonlinear PDEs

Wenjie Guo, Jianfeng Zhang, and Jia Zhuo

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Abstract

In this paper we propose a feasible numerical scheme for high-dimensional, fully nonlinear parabolic PDEs, which includes the quasi-linear PDE associated with a coupled FBSDE as a special case. Our paper is strongly motivated by the remarkable work Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322–1364] and stays in the paradigm of monotone schemes initiated by Barles and Souganidis [Asymptot. Anal. 4 (1991) 271–283]. Our scheme weakens a critical constraint imposed by Fahim, Touzi and Warin (2011), especially when the generator of the PDE depends only on the diagonal terms of the Hessian matrix. Several numerical examples, up to dimension 12, are reported.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 3 (2015), 1540-1580.

Dates
First available in Project Euclid: 23 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1427124136

Digital Object Identifier
doi:10.1214/14-AAP1030

Mathematical Reviews number (MathSciNet)
MR3325281

Zentralblatt MATH identifier
1321.65158

Subjects
Primary: 65C05: Monte Carlo methods
Secondary: 49L25: Viscosity solutions

Keywords
Monotone scheme least square regression Monte Carlo methods fully nonlinear PDEs viscosity solutions

Citation

Guo, Wenjie; Zhang, Jianfeng; Zhuo, Jia. A monotone scheme for high-dimensional fully nonlinear PDEs. Ann. Appl. Probab. 25 (2015), no. 3, 1540--1580. doi:10.1214/14-AAP1030. https://projecteuclid.org/euclid.aoap/1427124136


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