A SPARSE-GRID METHOD FOR MULTI-DIMENSIONAL BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

被引：35
作者：
Zhang, Guannan [1 ,2 ]
Gunzburger, Max [1 ]
Zhao, Weidong [3 ]
机构：
[1] Florida State Univ, Dept Comp Sci, Tallahassee, FL 32306 USA
[2] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN 37831 USA
[3] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL MATHEMATICS | 2013年 / 31卷 / 03期
基金：
美国能源部;
关键词：
Backward stochastic differential equations; Multi-step scheme; Gauss-Hermite quadrature rule; Adaptive hierarchical basis; Sparse grids; COLLOCATION METHOD; NUMERICAL-METHOD; THETA-SCHEME; INTEGRATION; INTERPOLATION;
D O I：
10.4208/jcm.1212-m4014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：221 / 248
页数：28
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