An Introductory Review of Time-Inconsistent Stochastic Optimal Control

This paper gives an introductory review of time-inconsistent stochastic optimal control. We mainly explain the reasons that result in the time inconsistency, and review the recent progresses in time-inconsistent stochastic linear-quadratic optimal control.

[1]  P. Samuelson A Note on Measurement of Utility , 1937 .

[2]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[3]  R. H. Strotz Myopia and Inconsistency in Dynamic Utility Maximization , 1955 .

[4]  H. McKean,et al.  A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[5]  M. Hp A class of markov processes associated with nonlinear parabolic equations. , 1966 .

[6]  R. Aumann,et al.  Some Thoughts on the Minimax Principle , 1972 .

[7]  D. Raphael,et al.  I: The Theory of Moral Sentiments , 1976 .

[8]  V. Yakubovich Abstract theory of optimal control. IV , 1979 .

[9]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[10]  David M. Kreps,et al.  Game Theory and Economic Modelling , 1992 .

[11]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[12]  David I. Laibson,et al.  Golden Eggs and Hyperbolic Discounting , 1997 .

[13]  Anthony A. Smith Consumption and Savings Decisions with Quasi-Geometric Discounting , 1999 .

[14]  Duan Li,et al.  Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation , 2000 .

[15]  Anthony A. Smith,et al.  Consumption--Savings Decisions with Quasi--Geometric Discounting , 2003 .

[16]  P. Caines,et al.  Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[17]  Ignacio Palacios-Huerta Time-Inconsistent Preferences in Adam Smith , 2003 .

[18]  I. Ekeland,et al.  Being serious about non-commitment: subgame perfect equilibrium in continuous time , 2006, math/0604264.

[19]  P. Lions,et al.  Mean field games , 2007 .

[20]  I. Ekeland,et al.  Investment and consumption without commitment , 2007, 0708.0588.

[21]  Minyi Huang,et al.  Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria , 2007, IEEE Transactions on Automatic Control.

[22]  Tao Li,et al.  Asymptotically Optimal Decentralized Control for Large Population Stochastic Multiagent Systems , 2008, IEEE Transactions on Automatic Control.

[23]  Tomas Bjork,et al.  A General Theory of Markovian Time Inconsistent Stochastic Control Problems , 2010 .

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

[25]  J. Yong A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem , 2011, 1204.1856.

[26]  Daniel Andersson,et al.  A Maximum Principle for SDEs of Mean-Field Type , 2011 .

[27]  Juan Li,et al.  Stochastic maximum principle in the mean-field controls , 2012, Autom..

[28]  J. Yong Deterministic time-inconsistent optimal control problems — an essentially cooperative approach , 2012 .

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

[30]  Hanqing Jin,et al.  Time-Inconsistent Stochastic Linear-Quadratic Control , 2011, SIAM J. Control. Optim..

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

[32]  J. Yong Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions , 2013, 1304.3964.

[33]  A. Bensoussan,et al.  Mean Field Games and Mean Field Type Control Theory , 2013 .

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

[35]  Quanyan Zhu,et al.  Risk-Sensitive Mean-Field Games , 2012, IEEE Transactions on Automatic Control.

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

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

[38]  Haiyang Wang,et al.  Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation , 2015 .

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

[40]  Zhiyong Yu,et al.  Time-Inconsistent Recursive Stochastic Optimal Control Problems , 2016, SIAM J. Control. Optim..

[41]  Hanqing Jin,et al.  Time-Inconsistent Stochastic Linear–Quadratic Control: Characterization and Uniqueness of Equilibrium , 2015, SIAM J. Control. Optim..

[42]  Jiaqin Wei Time-inconsistent optimal control problems with regime-switching , 2017 .

[43]  Huanshui Zhang,et al.  Time-inconsistent stochastic linear quadratic control for discrete-time systems , 2017, Science China Information Sciences.

[44]  Miroslav Krstic,et al.  Equilibrium Solutions of Multiperiod Mean-Variance Portfolio Selection , 2018, IEEE Transactions on Automatic Control.

[45]  Shanefrederick,et al.  Time Discounting and Time Preference : A Critical Review , 2022 .