Teugels鞅的Malliavin导数与平均场型随机极大值原理

Pub Date : 2023-09-11 DOI:10.1080/17442508.2023.2256506

Gaofeng Zong

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引用次数: 0

摘要

研究了一类平均场型随机控制问题，该问题的动力学由具有所有阶矩的一般lsamvy过程控制。为此，我们引入幂跃过程和相关的Teugels鞅，并给出对Teugels鞅的Malliavin导数。我们以平均场随机极大值原理的形式导出了控制问题的最优性的充分必要条件。

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Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle

We study the mean-field type stochastic control problem where the dynamics is governed by a general Lévy process with moments of all orders. For this, we introduce the power jump processes and the related Teugels martingales and give the Malliavin derivative with respect to Teugels martingales. We derive necessary and sufficient conditions for optimality of our control problem in the form of a mean-field stochastic maximum principle.

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