Volume 31, Issue 3
A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations

Guannan Zhang and Max Gunzburger & Weidong Zhao

10.4208/jcm.1212-m4014

J. Comp. Math., 31 (2013), pp. 221-248.

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  • 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.

  • History

Published online: 2013-06

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