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://doi.org/10.4208/nmtma.OA-2019-0137
UR - https://global-sci.org/intro/article_detail/nmtma/15444.html
KW - Forward backward stochastic differential equations, stochastic optimal control, stochastic maximum principle, projected quasi-Newton methods.
AB - <p style="text-align: justify;">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.</p>