A mean-field stochastic maximum principle via Malliavin calculus

被引：91
作者：
Meyer-Brandis, Thilo [1 ]
Oksendal, Bernt [1 ,2 ]
Zhou, Xun Yu [3 ,4 ]
机构：
[1] Univ Oslo, CMA, N-0316 Oslo, Norway
[2] Norwegian Sch Econ & Business Adm NHH, N-5045 Bergen, Norway
[3] Univ Oxford, Inst Math, Oxford OX1 3LB, England
[4] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
来源：
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2012年 / 84卷 / 5-6期
基金：
欧洲研究理事会;
关键词：
Malliavin calculus; maximum principle; stochastic control; mean-field type; jump diffusion; partial information; DIFFERENTIAL-EQUATIONS; PARTIAL INFORMATION; LEVY PROCESSES; PORTFOLIO;
D O I：
10.1080/17442508.2011.651619
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers a mean-field type stochastic control problem where the dynamics is governed by a controlled Ito-Levy process and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
引用
收藏
页码：643 / 666
页数：24
相关论文
共 50 条
[1]   A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward-backward systems [J].
Wang, Yan ;
Song, Aimin ;
Feng, Enmin .
ASIAN JOURNAL OF CONTROL, 2015, 17 (05) :1798-1809
[2]   Maximum principle via Malliavin calculus for regular-singular stochastic differential games [J].
Wang, Yan ;
Song, Aimin ;
Wang, Lei ;
Sun, Jie .
OPTIMIZATION LETTERS, 2018, 12 (06) :1301-1314
[3]   Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle [J].
Zong, Gaofeng .
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2024, 96 (02) :1072-1091
[4]   A Stochastic Maximum Principle for General Mean-Field Systems [J].
Buckdahn, Rainer ;
Li, Juan ;
Ma, Jin .
APPLIED MATHEMATICS AND OPTIMIZATION, 2016, 74 (03) :507-534
[5]   A Stochastic Maximum Principle for General Mean-Field Systems [J].
Rainer Buckdahn ;
Juan Li ;
Jin Ma .
Applied Mathematics & Optimization, 2016, 74 :507-534
[6]   Maximum principle via Malliavin calculus for regular-singular stochastic differential games [J].
Yan Wang ;
Aimin Song ;
Lei Wang ;
Jie Sun .
Optimization Letters, 2018, 12 :1301-1314
[7]   A STOCHASTIC MAXIMUM PRINCIPLE FOR GENERAL MEAN-FIELD SYSTEM WITH CONSTRAINTS [J].
Meherrem, Shahlar ;
Hafayed, Mokhtar .
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2025, 15 (03) :565-578
[8]   A General Stochastic Maximum Principle for SDEs of Mean-field Type [J].
Buckdahn, Rainer ;
Djehiche, Boualem ;
Li, Juan .
APPLIED MATHEMATICS AND OPTIMIZATION, 2011, 64 (02) :197-216
[9]   A General Stochastic Maximum Principle for SDEs of Mean-field Type [J].
Rainer Buckdahn ;
Boualem Djehiche ;
Juan Li .
Applied Mathematics & Optimization, 2011, 64 :197-216
[10]   STOCHASTIC MAXIMUM PRINCIPLE FOR WEIGHTED MEAN-FIELD SYSTEM [J].
Tang, Yanyan ;
Xiong, Jie .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (05) :1039-1053
12345