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Volume 10, Issue 2
A New Second-Order One-Step Scheme for Solving Decoupled FBSDES and Optimal Error Estimates

Yang Li, Jie Yang & Weidong Zhao

DOI: 10.4208/eajam.280519.180919

East Asian J. Appl. Math., 10 (2020), pp. 354-380.

Published online: 2020-04

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  • Abstract

A novel second-order numerical scheme for solving decoupled forward backward stochastic differential equations is proposed. Unlike known second-order schemes for such equations, the forward stochastic differential equations are approximated by a simplified weak order-2 Itô-Taylor scheme. This makes the method more implementable and enhances the accuracy. If the operators involved satisfy certain commutativity conditions, the scheme with quadratic convergence can be simplified, which is important in applications. The stability of the method is studied and second-order optimal error estimates are obtained.

  • Keywords

FBSDEs, simplified weak Itô-Taylor scheme, second-order scheme, error estimate.

  • AMS Subject Headings

60H35, 65C20, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wdzhao@sdu.edu.cn (Weidong Zhao)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-354, author = {Li , YangYang , Jie and Zhao , Weidong}, title = {A New Second-Order One-Step Scheme for Solving Decoupled FBSDES and Optimal Error Estimates}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {354--380}, abstract = {

A novel second-order numerical scheme for solving decoupled forward backward stochastic differential equations is proposed. Unlike known second-order schemes for such equations, the forward stochastic differential equations are approximated by a simplified weak order-2 Itô-Taylor scheme. This makes the method more implementable and enhances the accuracy. If the operators involved satisfy certain commutativity conditions, the scheme with quadratic convergence can be simplified, which is important in applications. The stability of the method is studied and second-order optimal error estimates are obtained.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280519.180919}, url = {http://global-sci.org/intro/article_detail/eajam/16131.html} }
TY - JOUR T1 - A New Second-Order One-Step Scheme for Solving Decoupled FBSDES and Optimal Error Estimates AU - Li , Yang AU - Yang , Jie AU - Zhao , Weidong JO - East Asian Journal on Applied Mathematics VL - 2 SP - 354 EP - 380 PY - 2020 DA - 2020/04 SN - 10 DO - http://doi.org/10.4208/eajam.280519.180919 UR - https://global-sci.org/intro/article_detail/eajam/16131.html KW - FBSDEs, simplified weak Itô-Taylor scheme, second-order scheme, error estimate. AB -

A novel second-order numerical scheme for solving decoupled forward backward stochastic differential equations is proposed. Unlike known second-order schemes for such equations, the forward stochastic differential equations are approximated by a simplified weak order-2 Itô-Taylor scheme. This makes the method more implementable and enhances the accuracy. If the operators involved satisfy certain commutativity conditions, the scheme with quadratic convergence can be simplified, which is important in applications. The stability of the method is studied and second-order optimal error estimates are obtained.

Li , YangYang , Jie and Zhao , Weidong. (2020). A New Second-Order One-Step Scheme for Solving Decoupled FBSDES and Optimal Error Estimates. East Asian Journal on Applied Mathematics. 10 (2). 354-380. doi:10.4208/eajam.280519.180919
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