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.
| Original language | English |
|---|---|
| Pages (from-to) | 221-248 |
| Number of pages | 28 |
| Journal | Journal of Computational Mathematics |
| Volume | 31 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2013 |
Keywords
- Adaptive hierarchical basis
- Backward stochastic differential equations
- Gauss-Hermite quadrature rule
- Multi-step scheme
- Sparse grids