ABSTRACT In this paper, we introduce a new class of backward doubly stochastic differential equations (in short BDSDE) called mean-field backward doubly stochastic differential equations (in short MFBDSDE) driven by Itô-Lévy processes and study the partial information optimal control problems for backward doubly stochastic systems driven by Itô-Lévy processes of mean-field type, in which the coefficients depend on not only the solution processes but also their expected values. First, using the method of contraction mapping, we prove the existence and uniqueness of the solutions to this kind of MFBDSDE. Then, by the method of convex variation and duality technique, we establish a sufficient and necessary stochastic maximum principle for the stochastic system. Finally, we illustrate our theoretical results by an application to a stochastic linear quadratic optimal control problem of a mean-field backward doubly stochastic system driven by Itô-Lévy processes.

中文翻译：

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由 Itô-Lévy 过程驱动的平均场后向双随机系统的优化控制

摘要 在本文中，我们介绍了一类新的后向双随机微分方程（简称 BDSDE），称为平均场后向双随机微分方程（简称 MFBDSDE），由 Itô-Lévy 过程驱动，并研究了由平均场类型的 Itô-Lévy 过程驱动的后向双随机系统，其中系数不仅取决于求解过程，还取决于它们的期望值。首先，利用收缩映射的方法，证明了这类MFBDSDE解的存在唯一性。然后，通过凸变分方法和对偶技术，我们建立了随机系统的充分必要的随机极大值原理。最后，