full
search.png

Search

close.png

Cancel

arrow
Volume 21, Issue 3
High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control

Weidong Zhao, Tao Zhou & Tao Kong

DOI: 10.4208/cicp.OA-2016-0056

Commun. Comput. Phys., 21 (2017), pp. 808-834.

Published online: 2018-04

Preview Purchase PDF 2258 32087

Cited by

google scholar semantic scholar
Export citation
  • Abstract

This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple ($Y_t$,$Z_t$,$A_t$,$Γ_t$) of the 2FBSDEs) are still of high order accuracy. Several numerical examples are given to show the effectiveness of the proposed numerical schemes. Applications of our numerical schemes to stochastic optimal control problems are also presented.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-21-808, author = {Weidong Zhao, Tao Zhou and Tao Kong}, title = {High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {3}, pages = {808--834}, abstract = {

This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple ($Y_t$,$Z_t$,$A_t$,$Γ_t$) of the 2FBSDEs) are still of high order accuracy. Several numerical examples are given to show the effectiveness of the proposed numerical schemes. Applications of our numerical schemes to stochastic optimal control problems are also presented.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0056}, url = {http://global-sci.org/intro/article_detail/cicp/11261.html} }
TY - JOUR T1 - High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control AU - Weidong Zhao, Tao Zhou & Tao Kong JO - Communications in Computational Physics VL - 3 SP - 808 EP - 834 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0056 UR - https://global-sci.org/intro/article_detail/cicp/11261.html KW - AB -

This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple ($Y_t$,$Z_t$,$A_t$,$Γ_t$) of the 2FBSDEs) are still of high order accuracy. Several numerical examples are given to show the effectiveness of the proposed numerical schemes. Applications of our numerical schemes to stochastic optimal control problems are also presented.

Weidong Zhao, Tao Zhou and Tao Kong. (2018). High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control. Communications in Computational Physics. 21 (3). 808-834. doi:10.4208/cicp.OA-2016-0056
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard