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

被引：0

作者：

Zong, Gaofeng ^{[1
,2
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Stat & Math, Jinan, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Stat & Math, Jinan 250014, Peoples R China

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2024年 / 96卷 / 02期

基金：

美国国家科学基金会;

关键词：

Teugels martingales; mean-field; Malliavin derivative; stochastic maximum principle; DIFFERENTIAL-EQUATIONS; SYSTEMS;

D O I：

10.1080/17442508.2023.2256506

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the mean-field type stochastic control problem where the dynamics is governed by a general Levy 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.

引用

页码：1072 / 1091

页数：20

共 22 条

[1]

Ahmed N. U., 2001, Commun. Appl. Anal, V5, P183

[2]

Anderson D., 2011, APPL MATH OPT, V58, P76

[3] A maximum principle for stochastic control with partial information [J].