摘要 : This paper studies linear quadratic social optimal problems with control input constraints, where both dynamics and costs involve the coupled term of states, and the diffusion terms contain control variables. In virtue of the vari... 展开 This paper studies linear quadratic social optimal problems with control input constraints, where both dynamics and costs involve the coupled term of states, and the diffusion terms contain control variables. In virtue of the variational method, we obtain the corresponding auxiliary stochastic control problem by introducing the limiting state-average process. Furthermore, we design a set of decentralized control strategies by using the stochastic maximum principle, which is given by a fully coupled non-linear mean-field forward-backward stochastic differential equation, and they are further shown to be asymptotically social optimality by perturbation analysis. As applications, we apply the theoretical results to deal with the optimal consumption problem and obtain the related optimal consumption strategy.(c) 2022 Elsevier B.V. All rights reserved. 收起