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 - <p style="text-align: justify;">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.</p>