Abstract
We now go on to study a class of time-inconsistent stop** problems in discrete time. We start by defining the concepts of Markovian stop** strategies and subgame-perfect Nash equilibrium stop** 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 stop** 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.
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References
Bayraktar, E., Zhang, J., & Zhou, Z. (2019). Time consistent stop** 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 stop**, 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 stop** 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
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Björk, T., Khapko, M., Murgoci, A. (2021). Time-Inconsistent Stop** 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
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DOI: https://doi.org/10.1007/978-3-030-81843-2_23
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