A MONOTONE SCHEME FOR HIGH-DIMENSIONAL FULLY NONLINEAR PDES

作者：Guo Wenjie^*; Zhang Jianfeng; Zhuo Jia

来源：Annals of Applied Probability, 2015, 25(3): 1540-1580.

DOI：10.1214/14-AAP1030

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

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.

• 出版日期2015-6
• 单位复旦大学