Maximum principle for conditional mean-field FBSDEs systems with regime-switching involving impulse controls

被引：2
作者：
Wu, Zhen [1 ]
Zhang, Yan [2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[2] Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 250100, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 530卷 / 02期
关键词：
Maximum principle; Regime-switching; Mean-field theory; Impulse control; STOCHASTIC DIFFERENTIAL-EQUATIONS; GAMES;
D O I：
10.1016/j.jmaa.2023.127720
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, a stochastic control problem for a forward-backward regime-switching system with mean-field interactions involving impulse controls is studied. One feature of this study lies in the conditional mean-field term used in the model. Necessary conditions for both regular and impulse controls are established via convex variational technique, and the verification theorems are obtained under appropriate convexity assumptions as well. A mean-variance investment and consumption example is discussed to test the validity of the theoretical results, and numerical simulations are also carried out to make the results clearer. & COPY; 2023 Elsevier Inc. All rights reserved.
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页数：25
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共 32 条
[1]   Mean-field backward stochastic differential equations and applications [J].
Agram, Nacira ;
Hu, Yaozhong ;
oksendal, Bernt .
SYSTEMS & CONTROL LETTERS, 2022, 162
[2]   A Maximum Principle for SDEs of Mean-Field Type [J].
Andersson, Daniel ;
Djehiche, Boualem .
APPLIED MATHEMATICS AND OPTIMIZATION, 2011, 63 (03) :341-356
[3]   Mean-Field-Type Games with Jump and Regime Switching [J].
Bensoussan, Alain ;
Djehiche, Boualem ;
Tembine, Hamidou ;
Yam, Sheung Chi Phillip .
DYNAMIC GAMES AND APPLICATIONS, 2020, 10 (01) :19-57
[4]   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
[5]   FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND CONTROLLED MCKEAN-VLASOV DYNAMICS [J].
Carmona, Rene ;
Delarue, Francois .
ANNALS OF PROBABILITY, 2015, 43 (05) :2647-2700
[6]   About the Pricing Equations in Finance [J].
Crepey, Stephane .
PARIS-PRINCETON LECTURES ON MATHEMATICAL FINANCE 2010, 2011, 2003 :63-203
[7]   Maximum principle for discrete-time stochastic control problem of mean-field type [J].
Dong, Bozhang ;
Nie, Tianyang ;
Wu, Zhen .
AUTOMATICA, 2022, 144
[8]   Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model [J].
Donnelly, Catherine .
APPLIED MATHEMATICS AND OPTIMIZATION, 2011, 64 (02) :155-169
[9]   STOCHASTIC DIFFERENTIAL UTILITY [J].
DUFFIE, D ;
EPSTEIN, LG .
ECONOMETRICA, 1992, 60 (02) :353-394
[10]   Zero-Sum Stochastic Differential Game in Finite Horizon Involving Impulse Controls [J].
El Asri, Brahim ;
Mazid, Sehail .
APPLIED MATHEMATICS AND OPTIMIZATION, 2020, 81 (03) :1055-1087
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