Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 221–248
Abstract
A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and (adaptive) hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1212-m4014
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 221–248
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Backward stochastic differential equations Multi-step scheme Gauss-Hermite quadrature rule Adaptive hierarchical basis Sparse grids.