On time-inconsistent stopping problems and mixed strategy stopping times

By Sören Christensen, Kristoffer Lindensjo. Stochastic Processes and their Applications, 2018

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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 Ito diffusion.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c33356fbd78ddc2328f0bdfc049376885731c0cd