Time-Consistent Stopping Under Decreasing Impatience

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