Mean-field team in backward linear-quadratic control problems with model uncertainty
摘要
This paper studies a class of LQ mean-field team problems driven by backward stochastic differential equations (BSDEs) with drift uncertainty. In this framework, agents cooperate through state-average to minimize a shared social cost functional. A notable innovation of this work is modeling agent state dynamics using BSDEs with uncertain generators. Unlike standard social optimal control frameworks that rely on forward stochastic differential equations, we model agent’s states dynamics using BSDEs, in which the terminal conditions are specified. Moreover, we consider the model uncertainty in the decision-making process. Accordingly, we construct the backward mean-field team problem under model uncertainty. We derive the worst-case disturbance and formulate the related social cost. Applying a forward backward version of person-by-person optimality, we construct an auxiliary control problem for each agent under the worst scenario and establish the robust decentralized social strategy. The well-posedness of such consistency condition system is obtained by the Riccati decoupling method. The related asymptotic social optimality is also verified.