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On the Time-Inconsistent Deterministic Linear-Quadratic Control

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Listed:
  • Hongyan Cai
  • Danhong Chen
  • Yunfei Peng
  • Wei Wei

Abstract

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general time-inconsistent deterministic LQ problem, where the inconsistency arises from non-exponential discount functions. By studying the solvability of the Riccati equation, we show the existence and uniqueness of the linear equilibrium for the time-inconsistent LQ problem.

Suggested Citation

  • Hongyan Cai & Danhong Chen & Yunfei Peng & Wei Wei, 2021. "On the Time-Inconsistent Deterministic Linear-Quadratic Control," Papers 2105.03670, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2105.03670
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    References listed on IDEAS

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    4. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    5. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    6. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
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