Partially observed mean-field game and related mean-field forward-backward stochastic differential equation

We study a linear-convex mean-field game with input constraints for partially observed forwardbackward system, where both types of mean-field terms, asynchronous style (state-averages) and synchronous style (state expectations), are considered. The observation is a controlled process, whose drift term is linear with respect to state and control variable. For the general case, by using the mean-field method and the backward separation approach, we obtain the decentralized optimal strategies through a Hamiltonian system and related Consistency Condition (CC), which are given by two types of mean-field forward-backward stochastic differential equations with filtering. In virtue of continuation method and discounting method, the well-posedness of such kind of equations is proved under two different conditions. For the linear-quadratic case under linear subspace constraints, we give the feedback representation of the decentralized optimal strategies, and the Riccati type CC system is also given. As one application, an assetliability management problem is solved. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.