摘要
In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs.In particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the literature.For the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.
基金
Ying Hu is partially supported by Lebesgue Center of Mathematics“Investissements d’avenir”Program(Grant No.ANR-11-LABX-0020-01)
ANR CAESARS(Grant No.ANR-15-CE05-0024)
ANR MFG(Grant No.ANR-16-CE40-0015-01)
Shanjian Tang is partially supported by the National Science Foundation of China(Grant Nos.11631004 and 12031009)
Zuo Quan Xu is partially supported by NSFC(Grant No.11971409)
Research Grants Council of Hong Kong(GRF,Grant No.15202421)
PolyU-SDU Joint Research Center on Financial Mathematics
CAS AMSS-POLYU Joint Laboratory of Applied Mathematics
Hong Kong Polytechnic University.
