On partial-information optimal singular control problem for mean-field stochastic differential equations driven by Teugels martingales measures

ABSTRACT This paper is concerned with partial-information mixed optimal stochastic continuous–singular control problem for mean-field stochastic differential equation driven by Teugels martingales and an independent Brownian motion, where the Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes. The control variable has two components; the first being absolutely continuous, and the second singular. Partial-information necessary and sufficient conditions of optimal continuous–singular control for these mean-field models are investigated. As an illustration, this paper studies a partial-information linear quadratic control problem of mean-field type involving continuous–singular control.

[1]  Syed Abbas,et al.  On Near-Optimal Mean-Field Stochastic Singular Controls: Necessary and Sufficient Conditions for Near-Optimality , 2014, J. Optim. Theory Appl..

[2]  Tak Kuen Siu,et al.  The maximum principle for a jump-diffusion mean-field model and its application to the mean–variance problem , 2013 .

[3]  J. Menaldi,et al.  On Singular Stochastic Control Problems for Diffusions with Jumps , 1983, 1983 American Control Conference.

[4]  Maoning Tang,et al.  Optimal variational principle for backward stochastic control systems associated with Lévy processes , 2010 .

[5]  Mokhtar Hafayed,et al.  Singular mean-field optimal control for forward-backward stochastic systems and applications to finance , 2014 .

[6]  Maximum principle for backward stochastic systems associated with Lévy processes under partial information , 2012, Proceedings of the 31st Chinese Control Conference.

[7]  Weihai Zhang,et al.  Stochastic Maximum Principle for Mean-Field Type Optimal Control Under Partial Information , 2014, IEEE Transactions on Automatic Control.

[8]  Zhen Wu,et al.  Stochastic differential equations and stochastic linear quadratic optimal control problem with Lévy processes , 2009, J. Syst. Sci. Complex..

[9]  Qingxin Meng,et al.  Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach , 2015, J. Comput. Appl. Math..

[10]  Hamidou Tembine,et al.  A stochastic maximum principle for risk-sensitive mean-field-type control , 2014, CDC.

[11]  Boris M. Miller,et al.  Maximum Principle for Singular Stochastic Control Problems , 2006, SIAM J. Control. Optim..

[12]  Ji-Feng Zhang,et al.  Mean Field Games for Large-Population Multiagent Systems with Markov Jump Parameters , 2012, SIAM J. Control. Optim..

[13]  Yuh-tai Ju.  SINGULAR OPTIMAL CONTROL , 1980 .

[14]  J. Menaldi,et al.  On singular stochastic control problems for diffusion with jumps , 1984 .

[15]  U. Haussmann,et al.  Singular Optimal Stochastic Controls II: Dynamic Programming , 1995 .

[16]  Boualem Djehiche,et al.  A General Stochastic Maximum Principle for SDEs of Mean-field Type , 2011 .

[17]  Jiongmin Yong,et al.  Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations , 2013, SIAM J. Control. Optim..

[18]  J. Yong.  A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations , 2011, 1110.1564.

[19]  Tao Li,et al.  Adaptive Mean Field Games for Large Population Coupled ARX Systems with Unknown Coupling Strength , 2013, Dynamic Games and Applications.

[20]  Jifeng Zhang,et al.  Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control , 2015, IEEE Transactions on Automatic Control.

[21]  Mokhtar Hafayed,et al.  A mean-field maximum principle for optimal control of forward–backward stochastic differential equations with Poisson jump processes , 2013 .

[22]  Yoshio Tabata,et al.  A stochastic linear-quadratic problem with Lévy processes and its application to finance , 2008 .

[23]  Feng Zhang.  Stochastic maximum principle for mixed regular-singular control problems of forward-backward systems , 2013, J. Syst. Sci. Complex..

[24]  Xun Li,et al.  Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case , 2015, Autom..

[25]  Luis H. R. Alvarez,et al.  Singular Stochastic Control, Linear Diffusions, and Optimal Stopping: A Class of Solvable Problems , 2000, SIAM J. Control. Optim..

[26]  U. Haussmann,et al.  Singular Optimal Stochastic Controls I: Existence , 1995 .

[27]  Xun Li,et al.  Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon , 2015, IEEE Transactions on Automatic Control.

[28]  Yaozhong Hu,et al.  Singular mean-field control games with applications to optimal harvesting and investment problems , 2014, 1406.1863.

[29]  Bernt Øksendal,et al.  Singular Stochastic Control and Optimal Stopping with Partial Information of Itô-Lévy Processes , 2012, SIAM J. Control. Optim..

[30]  Syed Abbas,et al.  A general maximum principle for mean-field stochastic differential equations with jump processes , 2013, 1301.7327.

[31]  Zhen Wu,et al.  Maximum principles for partially observed mean-field stochastic systems with application to financial engineering , 2014, CCC 2014.

[32]  Peng Shi,et al.  Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance , 2014, Autom..

[33]  Syed Abbas,et al.  On necessary and sufficient conditions for near-optimal singular stochastic controls , 2013, Optim. Lett..

[34]  S. Abbas,et al.  On mean-field stochastic maximum principle for near-optimal controls for Poisson jump diffusion with applications , 2014 .

[35]  U. Haussmann,et al.  The stochastic maximum principle for a singular control problem , 1994 .

[36]  Mokhtar Hafayed,et al.  A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control , 2013 .

[37]  S. Abbas,et al.  Stochastic Near-Optimal Singular Controls for Jump Diffusions: Necessary and Sufficient Conditions , 2013 .

[38]  MaoNing Tang,et al.  Necessary and sufficient conditions for optimal control of stochastic systems associated with Lévy processes , 2009, Science in China Series F: Information Sciences.

[39]  Xun Li,et al.  Discrete time mean-field stochastic linear-quadratic optimal control problems , 2013, Autom..