| Abstract: |
| In this paper, we focus on a type of linear-quadratic (LQ) mean-field game of stochastic differential equation (SDE) with terminal state constraint and common noise, where a coupling structure enters state equation, cost functional and constraint condition. First, by virtue of mean-field method, we introduce an auxiliary problem of the original game, which is a constrained optimal control problem. Second, by virtue of Lagrangian multiplier method and stochastic maximum principle, a decentralized control strategy depending on the optimal Lagrangian multiplier is derived. Finally, we prove that the decentralized control strategy obtained is an $\epsilon$-Nash equilibrium of the LQ mean-field game. As an application, we solve a financial problem and give some numerical results. |
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