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Volume 10, Issue 3
An Explicit Second Order Scheme for Decoupled Anticipated Forward Backward Stochastic Differential Equations

Yabing Sun & Weidong Zhao

DOI: 10.4208/eajam.271119.200220

East Asian J. Appl. Math., 10 (2020), pp. 566-593.

Published online: 2020-06

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  • Abstract

The Feynman-Kac formula and the Lagrange interpolation method are used in the construction of an explicit second order scheme for decoupled anticipated forward backward stochastic differential equations. The stability of the scheme is rigorously proved and error estimates are established. The scheme has the second order accuracy when weak order 2.0 Taylor scheme is employed to solve stochastic differential equations. Numerical tests confirm the theoretical findings.

  • Keywords

Anticipated forward backward stochastic differential equations, explicit scheme, error estimate, second order convergence.

  • AMS Subject Headings

60H35, 65C20, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-566, author = {Sun , Yabing and Zhao , Weidong}, title = {An Explicit Second Order Scheme for Decoupled Anticipated Forward Backward Stochastic Differential Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {566--593}, abstract = {

The Feynman-Kac formula and the Lagrange interpolation method are used in the construction of an explicit second order scheme for decoupled anticipated forward backward stochastic differential equations. The stability of the scheme is rigorously proved and error estimates are established. The scheme has the second order accuracy when weak order 2.0 Taylor scheme is employed to solve stochastic differential equations. Numerical tests confirm the theoretical findings.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.271119.200220}, url = {http://global-sci.org/intro/article_detail/eajam/16983.html} }
TY - JOUR T1 - An Explicit Second Order Scheme for Decoupled Anticipated Forward Backward Stochastic Differential Equations AU - Sun , Yabing AU - Zhao , Weidong JO - East Asian Journal on Applied Mathematics VL - 3 SP - 566 EP - 593 PY - 2020 DA - 2020/06 SN - 10 DO - http://doi.org/10.4208/eajam.271119.200220 UR - https://global-sci.org/intro/article_detail/eajam/16983.html KW - Anticipated forward backward stochastic differential equations, explicit scheme, error estimate, second order convergence. AB -

The Feynman-Kac formula and the Lagrange interpolation method are used in the construction of an explicit second order scheme for decoupled anticipated forward backward stochastic differential equations. The stability of the scheme is rigorously proved and error estimates are established. The scheme has the second order accuracy when weak order 2.0 Taylor scheme is employed to solve stochastic differential equations. Numerical tests confirm the theoretical findings.

Sun , Yabing and Zhao , Weidong. (2020). An Explicit Second Order Scheme for Decoupled Anticipated Forward Backward Stochastic Differential Equations. East Asian Journal on Applied Mathematics. 10 (3). 566-593. doi:10.4208/eajam.271119.200220
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