On time-inconsistent stopping problems and mixed strategy stopping times

Sören Christensen and Kristoffer Lindensjö

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2886-2917

Abstract: A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows the agents in the game to jointly choose the intensity function of a Cox process is introduced and motivated. A subgame perfect Nash equilibrium is defined. The equilibrium is characterized and other necessary and sufficient equilibrium conditions including a smooth fit result are proved. Existence and uniqueness are investigated. A mean–variance and a variance problem are studied. The state process is a general one-dimensional Itô diffusion.

Keywords: Cox process; Mean–variance criterion; Mixed strategies; Optimal stopping; Subgame perfect nash equilibrium; Time-inconsistency (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:5:p:2886-2917

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DOI: 10.1016/j.spa.2019.08.010

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