Dublin City University

We present a dynamic theory for time-inconsistent stopping problems. 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 imple-mentable
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 one-dimensional Bessel process under hyperbolic discounting, we illustrate our theory in an explicit manner.