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A deterministic linear quadratic time-inconsistent optimal control problem

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  • A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with a quadratic cost functional. A notion of time-consistent equilibrium strategy is introduced for the original time-inconsistent problem. Under certain conditions, we construct an equilibrium strategy which can be represented via a Riccati--Volterra integral equation system. Our approach is based on a study of multi-person hierarchical differential games.
    Mathematics Subject Classification: Primary: 49L20, 49N10, 49N70; Secondary: 91A23, 91A65.


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  • [1]

    S. Basak and G. Chabakauri, Dynamic mean-variance asset allocation, Preprint, London Business School, 2008.


    L. D. Berkovitz, "Optimal Control Theory," Applied Mathematical Sciences, Vol. 12, Springer-Verlag, New York-Heidelberg, 1974.


    T. Björk and A. MurgociA general theory of Markovian time inconsistent stochasitc control problem, working paper.


    E. V. Böhm-Bawerk, "The Positive Theory of Capital," Books for Libraries Press, Freeport, New York, 1891.


    I. Ekeland and A. Lazrak, Being serious about non-commitment: subgame perfect equilibrium in continuous time, preprint, Univ. British Columbia, 2008.


    I. Ekeland and T. Privu, Investment and consumption without commitment, preprint, Univ. British Columbia, 2007.


    S. M. Goldman, Consistent plans, Review of Economic Studies, 47 (1980), 533-537.doi: 10.2307/2297304.


    S. R. Grenadier and N. WangInvestment under uncertainty and time-inconsistent preferences, preprint.


    P. J. Herings and K. I. M. RohdeTime-inconsistent preferences in a general equilibriub model, preprint.


    D. Hume, "A Treatise of Human Nature," First Edition, 1739; Reprint, Oxford Univ. Press, New York, 1978.


    W. S. Jevons, "Theory of Political Economy," Mcmillan, London, 1871.


    P. Krusell and A. A. Smith, Jr., Consumption and saving decisions with quasi-geometric discounting, Econometrica, 71 (2003), 366-375.doi: 10.1111/1468-0262.00400.


    D. Laibson, Golden eggs and hyperbolic discounting, Quarterly J. Econ., 112 (1997), 443-477.doi: 10.1162/003355397555253.


    A. Malthus, An essay on the principle of population, 1826, "The Works of Thomas Robert Malthus" (Eds. E. A. Wrigley and D. Souden), 2 and 3, W. Pickering, London, 1986.


    J. Marin-Solano and J. Navas, Non-constant discounting in finite horizon: The free terminal time case, J. Economic Dynamics and Control, 33 (2009), 666-675.doi: 10.1016/j.jedc.2008.08.008.


    A. Marshall, "Principles of Economics," 1st ed., 1890; 8th ed., Macmillan, London, 1920.


    M. Miller and M. Salmon, Dynamic games and the time inconsistency of optimal policy in open economics, The Economic Journal, 95 (1985), 124-137.doi: 10.2307/2232876.


    I. Palacios-Huerta, Time-inconsistent preferences in Adam Smith and Davis Hume, History of Political Economy, 35 (2003), 241-268.doi: 10.1215/00182702-35-2-241.


    V. Pareto, "Manuel d'économie Politique," Girard and Brieve, Paris, 1909.


    B. Peleg and M. E. Yaari, On the existence of a consistent course of action when tastes are changing, Review of Economic Studies, 40 (1973), 391-401.doi: 10.2307/2296458.


    R. A. Pollak, Consistent planning, Review of Economic Studies, 35 (1968), 185-199.doi: 10.2307/2296548.


    A. Smith, "The Theory of Moral Sentiments," First Edition, 1759; Reprint, Oxford Univ. Press, 1976.


    R. H. Strotz, Myopia and inconsistency in dynamic utility maximization, Review of Econ. Studies, 23 (1955), 165-180.doi: 10.2307/2295722.


    L. Tesfatsion, Time inconsistency of benevolent government economics, J. Public Economics, 31 (1986), 25-52.doi: 10.1016/0047-2727(86)90070-8.


    J. YongA deterministic time-inconsistent optimal control problem -- An essentially cooperative approach, Acta Appl. Math. Sinica, to appear.


    J. Yong, and X. Y. Zhou, "Stochastic Controls: Hamiltonian Systems and HJB Equations," Applications of Mathematics (New York), 43, Springer-Verlag, New York, 1999.

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