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March  2011, 1(1): 83-118. doi: 10.3934/mcrf.2011.1.83

A deterministic linear quadratic time-inconsistent optimal control problem

Jiongmin Yong 1,

1. 

Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received  October 2010 Revised  November 2010 Published  March 2011

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.
Keywords: linear-quadratic optimal control problem, Time-inconsistency, multi-person hierarchical differential games, time-consistent equilibrium strategy, Riccati--Volterra integral equation system..
Mathematics Subject Classification: Primary: 49L20, 49N10, 49N70; Secondary: 91A23, 91A6.
Citation: Jiongmin Yong. A deterministic linear quadratic time-inconsistent optimal control problem. Mathematical Control & Related Fields, 2011, 1 (1) : 83-118. doi: 10.3934/mcrf.2011.1.83
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show all references

References:
[1]

Preprint, London Business School, 2008. Google Scholar

[2]

Applied Mathematical Sciences, Vol. 12, Springer-Verlag, New York-Heidelberg, 1974.  Google Scholar

[3]

T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochasitc control problem,, working paper., ().   Google Scholar

[4]

Books for Libraries Press, Freeport, New York, 1891. Google Scholar

[5]

preprint, Univ. British Columbia, 2008. Google Scholar

[6]

preprint, Univ. British Columbia, 2007. Google Scholar

[7]

Review of Economic Studies, 47 (1980), 533-537. doi: 10.2307/2297304.  Google Scholar

[8]

S. R. Grenadier and N. Wang, Investment under uncertainty and time-inconsistent preferences,, preprint., ().   Google Scholar

[9]

P. J. Herings and K. I. M. Rohde, Time-inconsistent preferences in a general equilibriub model,, preprint., ().   Google Scholar

[10]

First Edition, 1739; Reprint, Oxford Univ. Press, New York, 1978. Google Scholar

[11]

Mcmillan, London, 1871. Google Scholar

[12]

Econometrica, 71 (2003), 366-375. doi: 10.1111/1468-0262.00400.  Google Scholar

[13]

Quarterly J. Econ., 112 (1997), 443-477. doi: 10.1162/003355397555253.  Google Scholar

[14]

"The Works of Thomas Robert Malthus" (Eds. E. A. Wrigley and D. Souden), 2 and 3, W. Pickering, London, 1986. Google Scholar

[15]

J. Economic Dynamics and Control, 33 (2009), 666-675. doi: 10.1016/j.jedc.2008.08.008.  Google Scholar

[16]

1st ed., 1890; 8th ed., Macmillan, London, 1920. Google Scholar

[17]

The Economic Journal, 95 (1985), 124-137. doi: 10.2307/2232876.  Google Scholar

[18]

History of Political Economy, 35 (2003), 241-268. doi: 10.1215/00182702-35-2-241.  Google Scholar

[19]

Girard and Brieve, Paris, 1909. Google Scholar

[20]

Review of Economic Studies, 40 (1973), 391-401. doi: 10.2307/2296458.  Google Scholar

[21]

Review of Economic Studies, 35 (1968), 185-199. doi: 10.2307/2296548.  Google Scholar

[22]

First Edition, 1759; Reprint, Oxford Univ. Press, 1976. Google Scholar

[23]

Review of Econ. Studies, 23 (1955), 165-180. doi: 10.2307/2295722.  Google Scholar

[24]

J. Public Economics, 31 (1986), 25-52. doi: 10.1016/0047-2727(86)90070-8.  Google Scholar

[25]

J. Yong, A deterministic time-inconsistent optimal control problem -- An essentially cooperative approach,, Acta Appl. Math. Sinica, ().   Google Scholar

[26]

Applications of Mathematics (New York), 43, Springer-Verlag, New York, 1999.  Google Scholar

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