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High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control

Part of: Stochastic analysis Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  07 February 2017

Weidong Zhao ,
Tao Zhou  and
Tao Kong
Weidong Zhao
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China
Tao Zhou*
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Tao Kong*
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China
*
*Corresponding author. Email addresses:[email protected] (T. Zhou), [email protected] (W. Zhao)
*Corresponding author. Email addresses:[email protected] (T. Zhou), [email protected] (W. Zhao)
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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 (Yt,Zt,At,Γt) 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

Multistep schemessecond-order forward backward stochastic differential equationsstochastic optimal control

MSC classification

Secondary: 60H35: Computational methods for stochastic equations 65H20: Global methods, including homotopy approaches
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 808 - 834
Copyright
Copyright © Global-Science Press 2017 

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