IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2308.13850.html
   My bibliography  Save this paper

Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness

Author

Listed:
  • Yunfei Peng
  • Wei Wei

Abstract

In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from non-exponential discount functions. We characterize the solutions to the HJB equations using a class of Riccati equations with integral terms. By studying the uniqueness of solutions to the integro-differential Riccati equations, we prove the uniqueness of solutions to the equilibrium HJB equations.

Suggested Citation

  • Yunfei Peng & Wei Wei, 2023. "Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness," Papers 2308.13850, arXiv.org.
    • Handle: RePEc:arx:papers:2308.13850
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2308.13850
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Yu-Jui Huang & Zhou Zhou, 2021. "Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 428-451, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mariana Khapko, 2023. "Asset pricing with dynamically inconsistent agents," Finance and Stochastics, Springer, vol. 27(4), pages 1017-1046, October.
    2. Tim Kaiser & Lukas Menkhoff & Luis Oberrauch, 2022. "Is Patience Malleable via Educational Intervention? Evidence from Field Experiments," CESifo Working Paper Series 10080, CESifo.
    3. Kemptner, Daniel & Tolan, Songül, 2018. "The role of time preferences in educational decision making," Economics of Education Review, Elsevier, vol. 67(C), pages 25-39.
    4. Lillemo, Shuling Chen, 2014. "Measuring the effect of procrastination and environmental awareness on households' energy-saving behaviours: An empirical approach," Energy Policy, Elsevier, vol. 66(C), pages 249-256.
    5. Tasoff, Joshua & Letzler, Robert, 2014. "Everyone believes in redemption: Nudges and overoptimism in costly task completion," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PA), pages 107-122.
    6. John Y. Campbell, 2016. "Restoring Rational Choice: The Challenge of Consumer Financial Regulation," American Economic Review, American Economic Association, vol. 106(5), pages 1-30, May.
    7. Robert Gazzale & Julian Jamison & Alexander Karlan & Dean Karlan, 2013. "Ambiguous Solicitation: Ambiguous Prescription," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 1002-1011, January.
    8. Hinnosaar, Marit, 2016. "Time inconsistency and alcohol sales restrictions," European Economic Review, Elsevier, vol. 87(C), pages 108-131.
    9. Humphreys, Brad & Ruseski, Jane & Zhou, Li, 2015. "Physical Activity, Present Bias, and Habit Formation: Theory and Evidence from Longitudinal Data," Working Papers 2015-6, University of Alberta, Department of Economics.
    10. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    11. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    12. Min Gong & David Krantz & Elke Weber, 2014. "Why Chinese discount future financial and environmental gains but not losses more than Americans," Journal of Risk and Uncertainty, Springer, vol. 49(2), pages 103-124, October.
    13. Todd D. Gerarden & Richard G. Newell & Robert N. Stavins, 2017. "Assessing the Energy-Efficiency Gap," Journal of Economic Literature, American Economic Association, vol. 55(4), pages 1486-1525, December.
    14. Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
    15. Christopher D. Carroll, 2000. "Requiem for the Representative Consumer? Aggregate Implications of Microeconomic Consumption Behavior," American Economic Review, American Economic Association, vol. 90(2), pages 110-115, May.
    16. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
    17. Omar Galárraga & Sandra Sosa-Rubí & César Infante & Paul Gertler & Stefano Bertozzi, 2014. "Willingness-to-accept reductions in HIV risks: conditional economic incentives in Mexico," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(1), pages 41-55, January.
    18. Kimmich, Christian & Fischbacher, Urs, 2016. "Behavioral determinants of supply chain integration and coexistence," Journal of Forest Economics, Elsevier, vol. 25(C), pages 55-77.
    19. Stephen L. Cheung & Agnieszka Tymula & Xueting Wang, 2022. "Present bias for monetary and dietary rewards," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1202-1233, September.
    20. Anil Kumar, 2018. "Do Restrictions on Home Equity Extraction Contribute to Lower Mortgage Defaults? Evidence from a Policy Discontinuity at the Texas Border," American Economic Journal: Economic Policy, American Economic Association, vol. 10(1), pages 268-297, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2308.13850. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.