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
收藏
页码：1072 / 1091
页数：20
相关论文
共 22 条
  • [1] Ahmed N., 2001, Communications in Applied Analysis, V5, P183
  • [2] Anderson D., 2011, APPL MATH OPT, V58, P76
  • [3] A maximum principle for stochastic control with partial information
    Baghery, Fouzia
    Oksendal, Bernt
    [J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (03) : 705 - 717
  • [4] THE PARTIALLY OBSERVED STOCHASTIC MINIMUM PRINCIPLE
    BARAS, JS
    ELLIOTT, RJ
    KOHLMANN, M
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (06) : 1279 - 1292
  • [5] Bensoussan A., 1992, Stochastic Control of Partially Observable Systems
  • [6] Bertoin J., 1996, LEVY PROCESSES
  • [7] A General Stochastic Maximum Principle for SDEs of Mean-field Type
    Buckdahn, Rainer
    Djehiche, Boualem
    Li, Juan
    [J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2011, 64 (02) : 197 - 216
  • [8] Di Nunno G, 2009, UNIVERSITEXT, P1
  • [9] On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Levy Processes
    Hafayed, Mokhtar
    Abbas, Syed
    Abba, Abdelmadjid
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 167 (03) : 1051 - 1069
  • [10] Huang MY, 2006, COMMUN INF SYST, V6, P221
123