Optimal Equilibria for Multidimensional Time-Inconsistent Stopping Problems

Abstract

<div role="paragraph">We study an optimal stopping problem under nonexponential discounting, where the state process is a <em>multidimensional</em> continuous strong Markov process. The discount function is taken to be log subadditive, capturing <em>decreasing impatience</em> in behavioral economics. On the strength of probabilistic potential theory, we establish the existence of an optimal equilibrium among a sufficiently large collection of equilibria, consisting of finely closed equilibria satisfying a boundary condition. This generalizes the existence of optimal equilibria for one-dimensional stopping problems in prior literature.</div> &nbsp;

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