High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control (Communications in Computational Physics, 2018)
This is one of our series papers on multistep schemes for solving forwardbackward stochastic differential equations (FBSDEs) and related problems. Here weextend (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-orderFBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler methodis used to discretize the forward SDE, which dramatically reduces the entire computationalcomplexity. Moreover, it is shown that the usual quantities of interest (e.g., thesolution tuple ($Y_t$,$Z_t$,$A_t$,$Γ_t$) of the 2FBSDEs) are still of high order accuracy. Severalnumerical examples are given to show the effectiveness of the proposed numericalschemes. Applications of our numerical schemes to stochastic optimal control problemsare also presented.