In this article, we discuss an infinite horizon optimal control of the stochastic system with partial information, where the state is governed by a mean‐field stochastic differential delay equation driven by Teugels martingales associated with Lévy processes and an independent Brownian motion. First, we show the existence and uniqueness theorem for an infinite horizon mean‐field anticipated backward stochastic differential equation driven by Teugels martingales. Then applying different approaches for the underlying system, we establish two classes of stochastic maximum principles, which include two necessary conditions and two sufficient conditions for optimality, under a convex control domain. Moreover, compared with the finite horizon optimal control, we add the transversality conditions to the two kinds of stochastic maximum principles. Finally, using the stochastic maximum principle II, we settle an infinite horizon optimal consumption problem driven by Teugels martingales associated with Gamma processes.

中文翻译：

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局部信息下由Teugels martingales驱动的均场随机时滞系统的无限地平线最优控制

在本文中，我们讨论具有部分信息的随机系统的无限地平线最优控制，其中状态由与Lévy过程相关的Teugels martingales驱动的平均场随机微分延迟方程和独立的Brown运动控制。首先，我们证明了由Teugels martingales驱动的无限层均值预期后向随机微分方程的存在性和唯一性定理。然后对底层系统应用不同的方法，我们建立了两类随机最大原理，包括凸控制域下的两个最优性的两个必要条件和两个充分条件。此外，与有限水平最优控制相比，我们将横向条件添加到两种随机最大原理中。最后，