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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 nonexponential 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 subadditive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and integrability conditions. Although 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, a 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, 2020. "Optimal equilibria for time‐inconsistent stopping problems in continuous time," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1103-1134, July.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:3:p:1103-1134
    DOI: 10.1111/mafi.12229
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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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    4. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
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    7. 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.
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    Cited by:

    1. Erhan Bayraktar & Zhenhua Wang & Zhou Zhou, 2023. "Equilibria of time‐inconsistent stopping for one‐dimensional diffusion processes," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 797-841, July.
    2. Yu-Jui Huang & Zhou Zhou, 2022. "A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria," Finance and Stochastics, Springer, vol. 26(2), pages 301-334, April.
    3. Oumar Mbodji & Traian A. Pirvu, 2023. "Portfolio Time Consistency and Utility Weighted Discount Rates," Papers 2402.05113, arXiv.org.
    4. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    5. Shuoqing Deng & Xiang Yu & Jiacheng Zhang, 2023. "On time-consistent equilibrium stopping under aggregation of diverse discount rates," Papers 2302.07470, arXiv.org, revised Dec 2023.
    6. Zongxia Liang & Fengyi Yuan, 2021. "Weak equilibria for time-inconsistent control: with applications to investment-withdrawal decisions," Papers 2105.06607, arXiv.org, revised Jun 2023.

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