Highly Accurate Numerical Schemes for Stochastic Optimal Control via FBSDEs

Highly Accurate Numerical Schemes for Stochastic Optimal Control via FBSDEs

Year:    2020

Author:    Tao Zhou, Yu Fu, Weidong Zhao, Tao Zhou

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 296–319

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

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

Author Details

Tao Zhou

Yu Fu

Weidong Zhao

Tao Zhou