IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01116414.html
   My bibliography  Save this paper

Time-consistent stopping under decreasing impatience
[Arrêt temporellement cohérent sous impatience décroissante]

Author

Listed:
  • Yu-Jui Huang

    () (University of Colorado - Department of Applied Mathematics - University of Colorado [Boulder])

  • Adrien Nguyen-Huu

    () (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UM3 - Université Paul-Valéry - Montpellier 3 - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - INRA Montpellier - Institut national de la recherche agronomique [Montpellier] - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in Game Theory, and provides ``agent-specific'' results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model.

Suggested Citation

  • Yu-Jui Huang & Adrien Nguyen-Huu, 2017. "Time-consistent stopping under decreasing impatience
    [Arrêt temporellement cohérent sous impatience décroissante]
    ," Working Papers hal-01116414, HAL.
  • Handle: RePEc:hal:wpaper:hal-01116414
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01116414v4
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-01116414v4/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    2. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    3. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," Review of Economic Studies, Oxford University Press, vol. 23(3), pages 165-180.
    4. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    5. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    6. Hayashi, Takashi, 2009. "Stopping with anticipated regret," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 479-490, July.
    7. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    8. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non-stationary Time Preference and "Hyperbolic" Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    9. Noor, Jawwad, 2009. "Hyperbolic discounting and the standard model: Eliciting discount functions," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2077-2083, September.
    10. Sebastian Ebert & Philipp Strack, 2015. "Until the Bitter End: On Prospect Theory in a Dynamic Context," American Economic Review, American Economic Association, vol. 105(4), pages 1618-1633, April.
    11. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    12. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932, arXiv.org, revised Jan 2013.
    13. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    14. Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
    15. repec:dau:papers:123456789/11473 is not listed on IDEAS
    16. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    17. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    18. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    19. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    20. Noor, Jawwad, 2009. "Decreasing impatience and the magnitude effect jointly contradict exponential discounting," Journal of Economic Theory, Elsevier, vol. 144(2), pages 869-875, March.
    21. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu-Jui Huang & Zhou Zhou, 2018. "Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time," Papers 1809.09243, arXiv.org, revised Jan 2019.
    2. Yu-Jui Huang & Zhou Zhou, 2017. "Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time," Papers 1712.07806, arXiv.org, revised Oct 2018.
    3. Yu-Jui Huang & Zhou Zhou, 2017. "The Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case," Papers 1707.04981, arXiv.org, revised Dec 2018.
    4. Yu-Jui Huang & Adrien Nguyen-Huu & Xun Yu Zhou, 2018. "General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion," Working Papers hal-01954926, HAL.
    5. Yu-Jui Huang & Adrien Nguyen-Huu & Xun Yu Zhou, 2018. "General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion," CEE-M Working Papers hal-01954926, CEE-M, Universtiy of Montpellier, CNRS, INRA, Montpellier SupAgro.
    6. Yu-Jui Huang & Adrien Nguyen-Huu & Xun Yu Zhou, 2018. "General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion," CEE-M Working Papers 18-16, CEE-M, Universitiy of Montpellier, CNRS, INRA, Montpellier SupAgro.
    7. Yu-Jui Huang & Adrien Nguyen-Huu & Xun Yu Zhou, 2017. "General Stopping Behaviors of Naive and Non-Committed Sophisticated Agents, with Application to Probability Distortion," Papers 1709.03535, arXiv.org, revised Mar 2019.
    8. Marcel Nutz & Yuchong Zhang, 2019. "Conditional Optimal Stopping: A Time-Inconsistent Optimization," Papers 1901.05802, arXiv.org.
    9. Yu-Jui Huang & Adrien Nguyen-Huu & Xun Yu Zhou, 2017. "Stopping Behaviors of Naïve and Non-Committed Sophisticated Agents when They Distort Probability
      [Comportement d'arrêt des agents naïfs et sophistiqués sous distorsion des probabilités perçues]
      ," Working Papers hal-01586655, HAL.

    More about this item

    Keywords

    Time-inconsistency; Optimal Stopping; Decreasing impatience; Hyperbolic discounting; subgame perfect equilibrium; sequential game;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles

    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:hal:wpaper:hal-01116414. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.