Time-Consistent Stopping Under Decreasing Impatience

29 Pages Posted: 18 Feb 2015

See all articles by Yu-Jui Huang

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Adrien Nguyen Huu

Université Paris Dauphine

Date Written: February 13, 2015

Abstract

The paper presents a dynamic theory for time-inconsistent problems of optimal stopping. The theory is developed under the paradigm of expected discounted payoff, where the process to stop is continuous and Markovian. We introduce equilibrium stopping policies, which are implementable stopping rules that take into account the change of preferences over time. When the discount function induces decreasing impatience, we establish a constructive method to find equilibrium policies. A new class of stopping problems, involving equilibrium policies, is introduced, as opposed to classical optimal stopping. By studying the stopping of a BES(1) process under hyperbolic discounting, we illustrate our theory in an explicit manner.

Keywords: Time-inconsistency, Decreasing impatience, Optimal Stopping, Hyperbolic discounting, Markov subgame perfect equilibrium

JEL Classification: C73, G10

Suggested Citation

Huang, Yu-Jui and Nguyen Huu, Adrien, Time-Consistent Stopping Under Decreasing Impatience (February 13, 2015). Available at SSRN: https://ssrn.com/abstract=2565742 or http://dx.doi.org/10.2139/ssrn.2565742

Yu-Jui Huang (Contact Author)

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

Adrien Nguyen Huu

Université Paris Dauphine

Place du Maréchal de Lattre de Tassigny
Paris, 750016
France

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