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Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

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  • Yu-Jui Huang
  • Zhou Zhou

Abstract

For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub-additive and the state process is one-dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and integrability conditions. While there may exist other optimal equilibria, we show that they can differ from the constructed one in very limited ways. This leads to a sufficient condition for the uniqueness of optimal equilibria, up to some closedness condition. To illustrate our theoretic results, comprehensive analysis is carried out for three specific stopping problems, concerning asset liquidation and real options valuation. For each one of them, an optimal equilibrium is characterized through an explicit formula.

Suggested Citation

  • Yu-Jui Huang & Zhou Zhou, 2017. "Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time," Papers 1712.07806, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1712.07806
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    References listed on IDEAS

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    1. Yu‐Jui Huang & Adrien Nguyen‐Huu & Xun Yu Zhou, 2020. "General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 310-340, January.
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    5. 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.
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    12. 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.
    13. 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.
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    Cited by:

    1. Gad, Kamille Sofie Tågholt & Matomäki, Pekka, 2020. "Optimal variance stopping with linear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2349-2383.
    2. Christensen, Sören & Lindensjö, Kristoffer, 2020. "On time-inconsistent stopping problems and mixed strategy stopping times," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2886-2917.

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