General Optimal Stopping without Time Consistency

TL;DR

This paper introduces a novel framework for solving general dynamic optimal stopping problems without relying on time consistency, using backward iteration and equilibrium solutions, applicable to complex objective flows.

Contribution

It presents a new approach to handle time-inconsistent optimal stopping problems with a backward iteration method and equilibrium analysis, extending beyond traditional models.

Findings

Backward iteration effectively finds solutions in time-inconsistent settings.

Equilibrium solutions can be studied via a forward definition when iteration fails.

Framework applies to non-exponential discounting scenarios.

Abstract

In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A backward iteration is proposed to find the solution. The iteration works with an additional condition, which holds in interesting cases including the time inconsistency arising from non-exponential discounting. Even if the iteration does not work, the equilibrium solution can still be studied by a forward definition.