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Almost strong equilibria for time‐inconsistent stopping problems under finite horizon in continuous time

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  • Zhou Zhou

Abstract

We consider time‐inconsistent stopping problems for a continuous‐time Markov chain under finite time horizon with non‐exponential discounting. We provide an example indicating that strong equilibria may not exist in general. As a result, we propose a notion of equilibrium called almost strong equilibrium (ASE), which is a weak equilibrium and satisfies the condition of strong equilibria except at the boundary points of the associated stopping region. We provide an iteration procedure and show that this procedure leads to an ASE. Moreover, we prove that this ASE is the unique ASE among all regular stopping policies under finite horizon T

Suggested Citation

  • Zhou Zhou, 2024. "Almost strong equilibria for time‐inconsistent stopping problems under finite horizon in continuous time," Mathematical Finance, Wiley Blackwell, vol. 34(4), pages 1089-1122, October.
    • Handle: RePEc:bla:mathfi:v:34:y:2024:i:4:p:1089-1122
    DOI: 10.1111/mafi.12428
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