Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations

Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations

Year:    2024

Author:    Yafei Xu, Weidong Zhao

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 2 : pp. 463–493

Abstract

In this work, we consider Richardson extrapolation of the Euler scheme for backward stochastic differential equations (BSDEs). First, applying the Adomian decomposition to the nonlinear generator of BSDEs, we introduce a new system of BSDEs. Then we theoretically prove that the solution of the Euler scheme for BSDEs admits an asymptotic expansion, in which the coefficients in the expansions are the solutions of the system. Based on the expansion, we propose Richardson extrapolation algorithms for solving BSDEs. Finally, some numerical tests are carried out to verify our theoretical conclusions and to show the stability, efficiency and high accuracy of the algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2023-0134

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 2 : pp. 463–493

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Backward stochastic differential equations Euler scheme Adomian decomposition Richardson extrapolation asymptotic error expansion.

Author Details

Yafei Xu

Weidong Zhao