TY - JOUR
T1 - Optimal Control of SDEs with Expected Path Constraints and Related Constrained FBSDEs
AU - Hu, Ying
AU - Tang, Shanjian
AU - Xu, Zuoquan
N1 - Funding Information:
The three authors would like to thank both referees for their careful reading and helpful comments. Ying Hu is partially supported by Lebesgue Center of Mathematics “Investissements d’avenir” Program(Grant No. ANR-11-LABX-0020-01), by ANR CAESARS (Grant No. ANR-15-CE05-0024), and by 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), the Research Grants Council of Hong Kong (GRF, Grant No. 15202421), the PolyU-SDU Joint Research Center on Financial Mathematics, the CAS AMSS-POLYU Joint Laboratory of Applied Mathematics, and the Hong Kong Polytechnic University.
Publisher Copyright:
© Shandong University and AIMS, LLC.
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Expected path constraint
KW - Optimal stochastic control
KW - Reflected FBSDE
KW - Stochastic maximum principle
UR - http://www.scopus.com/inward/record.url?scp=85141417936&partnerID=8YFLogxK
U2 - 10.3934/puqr.2022020
DO - 10.3934/puqr.2022020
M3 - Journal article
AN - SCOPUS:85141417936
SN - 2095-9672
VL - 7
SP - 365
EP - 384
JO - Probability, Uncertainty and Quantitative Risk
JF - Probability, Uncertainty and Quantitative Risk
IS - 4
ER -