A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching

被引：0
作者：
Son L. Nguyen
George Yin
Dung T. Nguyen
机构：
[1] University of Puerto Rico,Department of Mathematics
[2] University of Connecticut,Department of Mathematics
[3] Ho Chi Minh City University of Technology - Vietnam National University,Department of Applied Mathematics, Faculty of Applied Science
来源：
Applied Mathematics & Optimization | 2021年 / 84卷
关键词：
Switching diffusion; Mean-field interaction; Maximum principle; Necessary condition; Sufficient condition; 60J25; 60J27; 60J60; 93E20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Focusing on regime-switching diffusions with mean-fields interactions, this paper is devoted to obtaining a general maximum principle. A main feature is that conditional mean-field is used in the controlled dynamic systems and the optimization process. Analysis of variational and adjoint equations using forward and backward stochastic differential equations with regime-switching and conditional mean-field is carried out. Necessary conditions for optimality are obtained without assuming the convexity of the control space. An example on conditional mean-variance portfolio selection with regime switching is given to illustrate the sufficient conditions for optimality.
引用
收藏
页码：3255 / 3294
页数：39
相关论文
共 77 条
[1]  
Andersson D(2011)A maximum principle for SDEs of mean-field type Appl. Math. Optim. 63 341-356
[2]  
Djehiche B(2011)A general stochastic maximum principle for SDEs of mean-field type Appl. Math. Optim. 64 197-216
[3]  
Buckdahn R(2017)A mean-field stochastic control problem with partial observations Ann. Appl. Probab. 27 3201-3245
[4]  
Djehiche B(2002)American options with regime switching Int. J. Theor. Appl. Finance 5 497-514
[5]  
Li J(2012)Quadratic risk minimization in a regime-switching model with portfolio constraints SIAM J. Control Optim. 50 2431-2461
[6]  
Buckdahn R(2016)Continuous time mean-variance portfolio optimization through the mean field approach ESAIM Probab. Stat. 20 30-44
[7]  
Li J(2004)Closed-form solutions for perpetual American put options with regime switching SIAM J. Appl. Math. 64 2034-2049
[8]  
Ma J(2012)Social optima in mean field LQG control: centralized and decentralized strategies IEEE Trans. Automat. Control 57 1736-1751
[9]  
Buffington J(2006)Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle Commun. Inf. Syst. 6 221-252
[10]  
Elliott RJ(2016)Mean field games for stochastic growth with relative utility Appl. Math. Optim. 74 643-668
12345678