Maximum Principle for Partial Observed Zero-Sum Stochastic Differential Game of Mean-Field SDEs
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- 英文论文题名：Maximum Principle for Partial Observed Zero-Sum Stochastic Differential Game of Mean-Field SDEs
- 论文作者：Maoning Tang ; Qingxin Meng
- 英文论文作者：Maoning Tang ; Qingxin Meng ; Department of Mathematical Sciences ; Huzhou University
- 年：2017
- 作者机构：Department of Mathematical Sciences,Huzhou University;
- 英文论文关键词：Zero-Sum Stochastic Differential Game ; Stochastic Maximum Principle ; Partial Observation ; Open-Loop Saddle ; Mean-Field
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O211.63
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：8
- 文件大小：284k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng(2016).
In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng(2016).
In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng(2016).
引文
[1]Andersson,D.,&Djehiche,B.,(2011).A maximum principle for SDEs of mean-field type.Applied Mathematics and Optimization,63,341-356.
[2]An,T.T.K.,&ksendal,B.(2008).Maximum principle for stochastic differential games with partial information.Journal of Optimization Theory and Applications,139(3),463-483.
[3]Baghery,F.,Baghery,F.,&?ksendal,B.(2007).A maximum principle for stochastic control with partial information.Stochastic Analysis and Applications,25(3),705-717.
[4]Basar,T.(2010).Lecture notes on non-cooperative game theory.Game Theory Module of the Graduate Program in Network Mathematics,3-6.
[5]Basar,T.,&Olsder,G.J.(1999).Dynamic noncooperative game theory(Vol.23).Siam.
[6]Bensoussan,A.,1983.Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions.Stochastics:An International Journal of Probability and Stochastic Processes,9(3),169-222.
[7]Berkovitz,L.D.,&Fleming,W.H.(1955).On differential games with integral payoff.Annals of Math.Study,(39),413-435.
[8]Buckdahn,R.,Li,J.,&Peng,S.,2009.Mean-field backward stochastic differential equations and related partial differential equations.Stochastic Processes and their Applications,119,3133-3154.
[9]Buckdahn,R.,Djehiche,B.,&Li,J.,2011.A general stochastic maximum principle for SDEs of mean-field type.Applied Mathematics and Optimization,64,197-216.
[10]Chala,A.(2014).The relaxed optimal control problem for Mean-Field SDEs systems and application.Automatica,50(3),924-930.
[11]Djehiche,B.,&Tembine,H.(2016).Risk-Sensitive MeanField Type Control Under Partial Observation.In Stochastics of Environmental and Financial Economics(pp.243-263).Springer International Publishing.
[12]Du,H.,Huang,J.,&Qin,Y.(2013).A stochastic maximum principle for delayed mean-field stochastic differential equations and its applications.IEEE Transactions on Automatic Control,38,3212-3217.
[13]R.Isaacs.Differential games,parts 1-4.The Rand Corpration,Research Memorandums Nos.RM-1391,RM-1411,RM-1486,1954-55
[14]Ekeland,I.,&Témam,R.,1976.Convex Analysis and Variational Problems,North-Holland,Amsterdam.
[15]Elliott,R.,Li,X.,&Ni,Y.H,2013.Discrete time meanfield stochastic linear-quadratic optimal control problems.Automatica,49(11),3222-3233.
[16]Hafayed,M.(2013).A mean-field maximum principle for optimal control of forward-backward stochastic differential equations with Poisson jump processes.International Journal of Dynamics and Control,1(4),300-315
[17]Hafayed,M.,Abbas,S.,&Abba,A.(2015).On mean-field partial information maximum principle of optimal control for stochastic systems with Levy processes.Journal of Optimization Theory and Applications,167(3),1051-1069.
[18]Li,J.,2012.Stochastic maximum principle in the mean-field controls.Automatica,48,366-373.
[19]Kallianpur,G.,2013.Stochastic filtering theory(Vol.13).Springer Science&Business Media.
[20]Kohlmann,M.,&Xiong,D.(2007).The mean-variance hedging of a defaultable option with partial information.Stochastic analysis and applications,25(4),869-893.
[21]Ma,H.,&Liu,B.,2017.Linear Quadratic Optimal Control Problem for Partially Observed Forward Backward Stochastic Differential Equations of Mean-Field Type.Asian Journal of Control.
[22]Meng,Q.,&Shen,Y.,2015.Optimal control of mean-field jump-diffusion systems with delay:A stochastic maximum principle approach.Journal of computational and applied mathematics,279,13-30.
[23]Meyer-Brandis,T.,?ksendal,B.,Zhou,X.Y.,2012.A meanfield stochastic maximum principle via Malliavin calculus.Stochastics,84,643-666.
[24]?ksendal,B.(2006).A universal optimal consumption rate for an insider.Mathematical Finance,16(1),119-129.
[25]Sethi,S.,&Thompson,G.(2000).Optimal Control Theory-Applications to Management Science and Economics,Springer.
[26]Shen,Y.,Meng,Q.,&Shi,P.,2014.Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance.Automatica,50(6),1565-1579.
[27]Shen,Y.,&Siu,T.K.,2013.The maximum principle for a jump-diffusion mean-field model and its application to the mean-variance problem.Nonlinear Analysis:Theory,Methods&Applications,86,58-73.
[28]Tang,M.,&Meng,Q.(2016).Partially Observed Optimal Control for Mean-Field SDEs.ar Xiv preprint ar Xiv:1610.02587.
[29]Tang,M.,&Meng,Q.(2010,July).Stochastic differential games of fully coupled forward-backward stochastic systems under partial information.In Proceedings of the 29th Chinese Control Conference(pp.1150-1155).IEEE.
[30]Tang,S.,1998.The maximum principle for partially observed optimal control of stochastic differential equations.SIAM Journal on Control and optimization,36(5),1596-1617
[31]Wang,G.,&Yu,Z.(2010).A Pontryagin’s maximum principle for non-zero sum differential games of BSDEs with applications.IEEE Transactions on Automatic Control,55(7),1742-1747.
[32]Wang,G.,&Yu,Z.(2012).A partial information non-zero sum differential game of backward stochastic differential equations with applications.Automatica,48(2),342-352.
[33]Wang,G.,&Wu,Z.,2009.The maximum principles for stochastic recursive optimal control problems under partial information.IEEE Transactions on Automatic control,54(6),1230-1242.
[34]Wang,G.,Wu,Z.,&Xiong,J.,2013.Maximum principles for forward-backward stochastic control systems with correlated state and observation noises.SIAM Journal on Control and Optimization,51(1),491-524.
[35]Wang,G.,Wu,Z.,&Xiong,J.,2015a.A linear-quadratic optimal control problem of forward-backward stochastic differential equations with partial information.IEEE Transactions on Automatic Control,60(11),2904-2916.
[36]Wang,G.,Wu,Z.,&Zhang,C.,2014a.Maximum principles for partially observed mean-field stochastic systems with application to financial engineering.In Control Conference(CCC),2014 33rd Chinese(pp.5357-5362).IEEE.
[37]Wang,G.,Wu,Z.,&Zhang,C.,2016.A partially observed optimal control problem for mean-field type forward-backward stochastic system.In Control Conference(CCC),2016 35th Chinese(pp.1781-1786).TCCT.
[38]Wang,G.,Xiao,H.,&Xing,G.,2015b.A class of optimal control problems for mean-field forward-backward stochastic systems with partial information.ar Xiv preprint ar Xiv:1509.03729.
[39]Wang,G.,Zhang,C.,&Zhang,W.,2014b.Stochastic maximum principle for mean-field type optimal control under partial information.IEEE Transactions on Automatic Control,59(2),522-528.
[40]Xiong,J.,Zhang,S.,&Zhuang,Y.(2016).A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance.ar Xiv preprint ar Xiv:1601.00538.
[2]An,T.T.K.,&ksendal,B.(2008).Maximum principle for stochastic differential games with partial information.Journal of Optimization Theory and Applications,139(3),463-483.
[3]Baghery,F.,Baghery,F.,&?ksendal,B.(2007).A maximum principle for stochastic control with partial information.Stochastic Analysis and Applications,25(3),705-717.
[4]Basar,T.(2010).Lecture notes on non-cooperative game theory.Game Theory Module of the Graduate Program in Network Mathematics,3-6.
[5]Basar,T.,&Olsder,G.J.(1999).Dynamic noncooperative game theory(Vol.23).Siam.
[6]Bensoussan,A.,1983.Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions.Stochastics:An International Journal of Probability and Stochastic Processes,9(3),169-222.
[7]Berkovitz,L.D.,&Fleming,W.H.(1955).On differential games with integral payoff.Annals of Math.Study,(39),413-435.
[8]Buckdahn,R.,Li,J.,&Peng,S.,2009.Mean-field backward stochastic differential equations and related partial differential equations.Stochastic Processes and their Applications,119,3133-3154.
[9]Buckdahn,R.,Djehiche,B.,&Li,J.,2011.A general stochastic maximum principle for SDEs of mean-field type.Applied Mathematics and Optimization,64,197-216.
[10]Chala,A.(2014).The relaxed optimal control problem for Mean-Field SDEs systems and application.Automatica,50(3),924-930.
[11]Djehiche,B.,&Tembine,H.(2016).Risk-Sensitive MeanField Type Control Under Partial Observation.In Stochastics of Environmental and Financial Economics(pp.243-263).Springer International Publishing.
[12]Du,H.,Huang,J.,&Qin,Y.(2013).A stochastic maximum principle for delayed mean-field stochastic differential equations and its applications.IEEE Transactions on Automatic Control,38,3212-3217.
[13]R.Isaacs.Differential games,parts 1-4.The Rand Corpration,Research Memorandums Nos.RM-1391,RM-1411,RM-1486,1954-55
[14]Ekeland,I.,&Témam,R.,1976.Convex Analysis and Variational Problems,North-Holland,Amsterdam.
[15]Elliott,R.,Li,X.,&Ni,Y.H,2013.Discrete time meanfield stochastic linear-quadratic optimal control problems.Automatica,49(11),3222-3233.
[16]Hafayed,M.(2013).A mean-field maximum principle for optimal control of forward-backward stochastic differential equations with Poisson jump processes.International Journal of Dynamics and Control,1(4),300-315
[17]Hafayed,M.,Abbas,S.,&Abba,A.(2015).On mean-field partial information maximum principle of optimal control for stochastic systems with Levy processes.Journal of Optimization Theory and Applications,167(3),1051-1069.
[18]Li,J.,2012.Stochastic maximum principle in the mean-field controls.Automatica,48,366-373.
[19]Kallianpur,G.,2013.Stochastic filtering theory(Vol.13).Springer Science&Business Media.
[20]Kohlmann,M.,&Xiong,D.(2007).The mean-variance hedging of a defaultable option with partial information.Stochastic analysis and applications,25(4),869-893.
[21]Ma,H.,&Liu,B.,2017.Linear Quadratic Optimal Control Problem for Partially Observed Forward Backward Stochastic Differential Equations of Mean-Field Type.Asian Journal of Control.
[22]Meng,Q.,&Shen,Y.,2015.Optimal control of mean-field jump-diffusion systems with delay:A stochastic maximum principle approach.Journal of computational and applied mathematics,279,13-30.
[23]Meyer-Brandis,T.,?ksendal,B.,Zhou,X.Y.,2012.A meanfield stochastic maximum principle via Malliavin calculus.Stochastics,84,643-666.
[24]?ksendal,B.(2006).A universal optimal consumption rate for an insider.Mathematical Finance,16(1),119-129.
[25]Sethi,S.,&Thompson,G.(2000).Optimal Control Theory-Applications to Management Science and Economics,Springer.
[26]Shen,Y.,Meng,Q.,&Shi,P.,2014.Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance.Automatica,50(6),1565-1579.
[27]Shen,Y.,&Siu,T.K.,2013.The maximum principle for a jump-diffusion mean-field model and its application to the mean-variance problem.Nonlinear Analysis:Theory,Methods&Applications,86,58-73.
[28]Tang,M.,&Meng,Q.(2016).Partially Observed Optimal Control for Mean-Field SDEs.ar Xiv preprint ar Xiv:1610.02587.
[29]Tang,M.,&Meng,Q.(2010,July).Stochastic differential games of fully coupled forward-backward stochastic systems under partial information.In Proceedings of the 29th Chinese Control Conference(pp.1150-1155).IEEE.
[30]Tang,S.,1998.The maximum principle for partially observed optimal control of stochastic differential equations.SIAM Journal on Control and optimization,36(5),1596-1617
[31]Wang,G.,&Yu,Z.(2010).A Pontryagin’s maximum principle for non-zero sum differential games of BSDEs with applications.IEEE Transactions on Automatic Control,55(7),1742-1747.
[32]Wang,G.,&Yu,Z.(2012).A partial information non-zero sum differential game of backward stochastic differential equations with applications.Automatica,48(2),342-352.
[33]Wang,G.,&Wu,Z.,2009.The maximum principles for stochastic recursive optimal control problems under partial information.IEEE Transactions on Automatic control,54(6),1230-1242.
[34]Wang,G.,Wu,Z.,&Xiong,J.,2013.Maximum principles for forward-backward stochastic control systems with correlated state and observation noises.SIAM Journal on Control and Optimization,51(1),491-524.
[35]Wang,G.,Wu,Z.,&Xiong,J.,2015a.A linear-quadratic optimal control problem of forward-backward stochastic differential equations with partial information.IEEE Transactions on Automatic Control,60(11),2904-2916.
[36]Wang,G.,Wu,Z.,&Zhang,C.,2014a.Maximum principles for partially observed mean-field stochastic systems with application to financial engineering.In Control Conference(CCC),2014 33rd Chinese(pp.5357-5362).IEEE.
[37]Wang,G.,Wu,Z.,&Zhang,C.,2016.A partially observed optimal control problem for mean-field type forward-backward stochastic system.In Control Conference(CCC),2016 35th Chinese(pp.1781-1786).TCCT.
[38]Wang,G.,Xiao,H.,&Xing,G.,2015b.A class of optimal control problems for mean-field forward-backward stochastic systems with partial information.ar Xiv preprint ar Xiv:1509.03729.
[39]Wang,G.,Zhang,C.,&Zhang,W.,2014b.Stochastic maximum principle for mean-field type optimal control under partial information.IEEE Transactions on Automatic Control,59(2),522-528.
[40]Xiong,J.,Zhang,S.,&Zhuang,Y.(2016).A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance.ar Xiv preprint ar Xiv:1601.00538.
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