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.Comment: Published at http://dx.doi.org/10.1214/14-AAP1030 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.