Abstract
We now go on to study a class of time-inconsistent stopping problems in discrete time. We start by defining the concepts of Markovian stopping strategies and subgame-perfect Nash equilibrium stopping strategies. Following similar steps to those in the control case, we then proceed to derive an extension of the standard Wald–Bellman equation to a non-standard extended system that allows for the determination of the equilibrium value function and the equilibrium stopping strategy. Examples studied at the end of the chapter include a time-inconsistent version of a simple secretary problem and a procrastination problem for a time-inconsistent agent who decides when to complete a task.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bayraktar, E., Zhang, J., & Zhou, Z. (2019). Time consistent stopping for the mean-standard deviation problem—The discrete time case. SIAM Journal on Financial Mathematics, 10(3), 667–697.
Bayraktar, E., & Zhou, Z. (2016). Arbitrage, hedging and utility maximization using semi-static trading strategies with American options. The Annals of Applied Probability, 26(6), 3531–3558.
Carroll, G. D., Choi, J. J., Laibson, D., Madrian, B. C., & Metrick, A. (2009). Optimal defaults and active decisions. The Quarterly Journal of Economics, 124(4), 1639–1674.
Christensen, S., & Lindensjö, K. (2020b). Time-inconsistent stopping, myopic adjustment and equilibrium stability: with a mean-variance application. Banach Center Publications, 122, 53–76.
Huang, Y.-J., & Zhou, Z. (2019). The optimal equilibrium for time-inconsistent stopping problems—the discrete-time case. SIAM Journal on Control and Optimization, 57(1), 590–609.
Huang, Y.-J., & Zhou, Z. (2021). A time-inconsistent Dynkin game: From intra-personal to inter-personal equilibria. Working paper. Available at https://arxiv.org/abs/2101.00343
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Björk, T., Khapko, M., Murgoci, A. (2021). Time-Inconsistent Stopping in Discrete Time. In: Time-Inconsistent Control Theory with Finance Applications. Springer Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-81843-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-81843-2_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81842-5
Online ISBN: 978-3-030-81843-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)