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Volume 5, Issue 4
Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

Jie Yang & Weidong Zhao

DOI: 10.4208/eajam.280515.211015a

East Asian J. Appl. Math., 5 (2015), pp. 387-404.

Published online: 2018-02

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  • Abstract

Convergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FBSDEs) that arises in finance and stochastic control. The corresponding $k$-step scheme admits a $k$-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

  • Keywords

Convergence analysis, multistep schemes, forward-backward stochastic differential equations.

  • AMS Subject Headings

60H35, 65C20, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-387, author = {Jie Yang and Weidong Zhao}, title = {Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {4}, pages = {387--404}, abstract = {

Convergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FBSDEs) that arises in finance and stochastic control. The corresponding $k$-step scheme admits a $k$-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280515.211015a}, url = {http://global-sci.org/intro/article_detail/eajam/10826.html} }
TY - JOUR T1 - Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation AU - Jie Yang & Weidong Zhao JO - East Asian Journal on Applied Mathematics VL - 4 SP - 387 EP - 404 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.280515.211015a UR - https://global-sci.org/intro/article_detail/eajam/10826.html KW - Convergence analysis, multistep schemes, forward-backward stochastic differential equations. AB -

Convergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FBSDEs) that arises in finance and stochastic control. The corresponding $k$-step scheme admits a $k$-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

Jie Yang and Weidong Zhao. (2018). Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation. East Asian Journal on Applied Mathematics. 5 (4). 387-404. doi:10.4208/eajam.280515.211015a
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