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

作者：Zhang, Guannan^*; Gunzburger, Max; Zhao, Weidong

来源：Journal of Computational Mathematics, 2013, 31(3): 221-248.

DOI：10.4208/jcm.1212-m4014

• Backward stochastic differential equations
• Multi-step scheme
• Gauss-Hermite quadrature rule
• Adaptive hierarchical basis
• Sparse grids

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.

• 出版日期2013-5
• 单位山东大学