TY - JOUR
T1 - A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations
AU - Guannan Zhang, Max Gunzburger & Weidong Zhao
JO - Journal of Computational Mathematics
VL - 3
SP - 221
EP - 248
PY - 2013
DA - 2013/06
SN - 31
DO - http://doi.org/10.4208/jcm.1212-m4014
UR - https://global-sci.org/intro/article_detail/jcm/9732.html
KW - Backward stochastic differential equations, Multi-step scheme, Gauss-Hermite
quadrature rule, Adaptive hierarchical basis, Sparse grids.
AB - <p style="text-align: justify;">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.</p>