Computing the maximum solution of second order partial differential systems related to stochastic optimal control

2003 ◽  
Author(s):  
E. Rofman
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Second Order ◽  
Partial Differential ◽  
Differential Systems ◽  
Maximum Solution

scholarly journals On a Class of Forward-Backward Stochastic Differential Systems in Infinite Dimensions

2007 ◽  
Vol 2007 ◽  
pp. 1-33 ◽  
Author(s):  
Giuseppina Guatteri
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Stochastic Optimal Control ◽  
Large Time ◽  
Regularity Property ◽  
Time Interval ◽  
Infinite Dimensions ◽  
Differential Systems ◽  
Stochastic Optimal Control Problem ◽  
Fully Coupled

We prove that a class of fully coupled forward-backward systems in infinite dimensions has a local unique solution. After studying the regularity property of the solution, we prove that for a peculiar class of systems arising in the theory of stochastic optimal control, the solution exists in arbitrary large time interval. Finally, we investigate the connection between the solution to the systems and a stochastic optimal control problem.

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

2017 ◽  
Vol 21 (3) ◽  
pp. 808-834 ◽  
Author(s):  
Weidong Zhao ◽  
Tao Zhou ◽  
Tao Kong
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Euler Method ◽  
Second Order ◽  
High Order ◽  
High Order Accuracy ◽  
Numerical Schemes ◽  
Order Accuracy ◽  
Quantities Of Interest

AbstractThis 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.

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