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Volume 17, Issue 1
An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps

Yabing Sun, Jie Yang & Weidong Zhao

DOI: 10.4208/nmtma.OA-2023-0048

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 243-274.

Published online: 2024-02

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  • Abstract

In this work, we propose an explicit second order scheme for decoupled mean-field forward backward stochastic differential equations with jumps. The stability and the rigorous error estimates are presented, which show that the proposed scheme yields a second order rate of convergence, when the forward mean-field stochastic differential equation is solved by the weak order 2.0 Itô-Taylor scheme. Numerical experiments are carried out to verify the theoretical results.

  • Keywords

Mean-field forward backward stochastic differential equation with jumps, stability analysis, error estimates.

  • AMS Subject Headings

65C30, 60H10, 60H35, 65C05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-243, author = {Sun , YabingYang , Jie and Zhao , Weidong}, title = {An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {1}, pages = {243--274}, abstract = {

In this work, we propose an explicit second order scheme for decoupled mean-field forward backward stochastic differential equations with jumps. The stability and the rigorous error estimates are presented, which show that the proposed scheme yields a second order rate of convergence, when the forward mean-field stochastic differential equation is solved by the weak order 2.0 Itô-Taylor scheme. Numerical experiments are carried out to verify the theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0048}, url = {http://global-sci.org/intro/article_detail/nmtma/22917.html} }
TY - JOUR T1 - An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps AU - Sun , Yabing AU - Yang , Jie AU - Zhao , Weidong JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 243 EP - 274 PY - 2024 DA - 2024/02 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0048 UR - https://global-sci.org/intro/article_detail/nmtma/22917.html KW - Mean-field forward backward stochastic differential equation with jumps, stability analysis, error estimates. AB -

In this work, we propose an explicit second order scheme for decoupled mean-field forward backward stochastic differential equations with jumps. The stability and the rigorous error estimates are presented, which show that the proposed scheme yields a second order rate of convergence, when the forward mean-field stochastic differential equation is solved by the weak order 2.0 Itô-Taylor scheme. Numerical experiments are carried out to verify the theoretical results.

Sun , YabingYang , Jie and Zhao , Weidong. (2024). An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps. Numerical Mathematics: Theory, Methods and Applications. 17 (1). 243-274. doi:10.4208/nmtma.OA-2023-0048
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