Richardson Extrapolation of the Crank-Nicolson Scheme for Backward Stochastic Differential Equations
Year: 2024
Author: Yafei Xu, Weidong Zhao
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 268–294
Abstract
In this work, we consider Richardson extrapolation of the Crank-Nicolson (CN) 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 CN scheme for BSDEs admits an asymptotic expansion with its coefficients the solutions of the new system of BSDEs. 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/ijnam2024-1011
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 268–294
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Backward stochastic differential equations Crank-Nicolson scheme Adomian decomposition Richardson extrapolation asymptotic error expansion.