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Deterministic time-inconsistent optimal control problems — an essentially cooperative approach

Deterministic time-inconsistent optimal control problems — an essentially cooperative approach A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Deterministic time-inconsistent optimal control problems — an essentially cooperative approach

Yong, Jiong-min
Acta Mathematicae Applicatae Sinica , Volume 28 (1) – Dec 13, 2011
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30 pages

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0120-3
Publisher site
See Article on Publisher Site

Abstract

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Dec 13, 2011

References

  • Dynamic mean-variance asset allocation
    Basak, S.; Chabakauri, G.
  • Optimal control theory
    Berkovitz, L.D.
  • The positive theory of capital
    Böhm-Bawerk, E.V.
  • Investment and consumption without commitment
    Ekeland, I.; Privu, T.
  • Consistent plans
    Goldman, S.M.
  • Investment under uncertainty and time-inconsistent preferences
    Grenadier, S.R.; Wang, N.
  • Time-inconsistent preferences in a general equilibriub model
    Herings, P.J.; Rohde, K.I.M.
  • Theory of Political Economy
    Jevons, W.S.
  • Consumption and saving decisions with quasi-geometric discounting
    Krusell, P.; Smith, A.A.
  • Golden eggs and hyperbolic discounting
    Laibson, D.
  • The Works of Thomas Robert Malthus
    Malthus, A.
  • Non-constant discounting in finite horizon: the free terminal time case
    Marin-Solano, J.; Navas, J.
  • Dynamic games and the time inconsistency of optimal policy in open economics
    Miller, M.; Salmon, M.
  • Time-inconsistent preferences in Adam Smith and Davis Hume
    Palacios-Huerta, I.
  • Manuel d’économie politique
    Pareto, V.
  • On the existence of a consistent course of action when tastes are changing
    Peleg, B.; Yaari, M.E.
  • Consistent planning
    Pollak, R.A.
  • Myopia and inconsistency in dynamic utility maximization
    Strotz, R.H.
  • Time inconsistency of benevolent government economics
    Tesfatsion, L.
  • Stochastic Controls: Hamiltonian Systems and HJB Equations
    Yong, J.; Zhou, X.Y.