Volume 13, Issue 2
Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs

Yu Fu, Weidong Zhao & Tao Zhou

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 296-319.

Published online: 2020-03

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  • 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.


  • Keywords

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

  • AMS Subject Headings

60H35, 93E20, 93E25, 49M29, 65C20, 65K15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

nielf fu@sdust.edu.cn (Yu Fu)

wdzhao@sdu.edu.cn (Weidong Zhao)

tzhou@lsec.cc.ac.cn (Tao Zhou)

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@Article{NMTMA-13-296, author = {Fu , Yu and Zhao , Weidong and Zhou , Tao }, title = {Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {296--319}, 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.


}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0137}, url = {http://global-sci.org/intro/article_detail/nmtma/15444.html} }
TY - JOUR T1 - Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs AU - Fu , Yu AU - Zhao , Weidong AU - Zhou , Tao JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 296 EP - 319 PY - 2020 DA - 2020/03 SN - 13 DO - http://dor.org/10.4208/nmtma.OA-2019-0137 UR - https://global-sci.org/intro/nmtma/15444.html KW - Forward backward stochastic differential equations, stochastic optimal control, stochastic maximum principle, projected quasi-Newton methods. AB -

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.


Yu Fu, Weidong Zhao & Tao Zhou. (2020). Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 296-319. doi:10.4208/nmtma.OA-2019-0137
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