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A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations

A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations
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Year:    2013

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 221–248

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1212-m4014

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 221–248

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

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

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