Highly Accurate Numerical Schemes for Stochastic Optimal Control via FBSDEs

Authors

  • Yu Fu College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China, and School of Mathematics & Institute of Finance, Shandong University, Jinan 250100, Shandong, China
  • Weidong Zhao School of Mathematics, Shandong University, Jinan, Shandong 250100, China
  • Tao Zhou CMIS & LSEC, Institute of Computational Mathematics and Scientific/ Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

DOI:

https://doi.org/10.4208/nmtma.OA-2019-0137

Keywords:

Forward backward stochastic differential equations, stochastic optimal control, stochastic maximum principle, projected quasi-Newton methods.

Abstract

This work is concerned with numerical schemes for stochastic optimal control problems (SOCPs) by means of forward backward stochastic differential equations (FBSDEs). We first convert the stochastic optimal control problem into an equivalent stochastic optimality system of FBSDEs. Then we design an efficient second order FBSDE solver and an quasi-Newton type optimization solver for the resulting system. It is noticed that our approach admits the second order rate of convergence even when the state equation is approximated by the Euler scheme. Several numerical examples are presented to illustrate the effectiveness and the accuracy of the proposed numerical schemes.

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Published

2020-03-09

Issue

Vol. 13 No. 2 (2020)

Section

Articles