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Volume 17, Issue 2
Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations

Yafei Xu & Weidong Zhao

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 463-493.

Published online: 2024-05

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  • 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.

  • AMS Subject Headings

65C30, 60H10, 60H35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-463, author = {Xu , Yafei and Zhao , Weidong}, title = {Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0134}, url = {http://global-sci.org/intro/article_detail/nmtma/23108.html} }
TY - JOUR T1 - Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations AU - Xu , Yafei AU - Zhao , Weidong JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 463 EP - 493 PY - 2024 DA - 2024/05 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0134 UR - https://global-sci.org/intro/article_detail/nmtma/23108.html KW - Backward stochastic differential equations, Euler scheme, Adomian decomposition, Richardson extrapolation, asymptotic error expansion. AB -

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.

Xu , Yafei and Zhao , Weidong. (2024). Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 17 (2). 463-493. doi:10.4208/nmtma.OA-2023-0134
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