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Time-consistent stopping under decreasing impatience

Yu-Jui Huang () and Adrien Nguyen-Huu ()
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Yu-Jui Huang: University of Colorado

Finance and Stochastics, 2018, vol. 22, issue 1, 69-95

Abstract: 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.

Keywords: Time inconsistency; Optimal stopping; Hyperbolic discounting; Decreasing impatience; Subgame-perfect Nash equilibrium; Iterative approach; 60G40; 91B06 (search for similar items in EconPapers)
JEL-codes: C61 D81 D90 G02 (search for similar items in EconPapers)
Date: 2018
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