Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

TL;DR

This paper investigates the existence and uniqueness of optimal equilibria in infinite-horizon continuous-time stopping problems with non-exponential discounting, providing explicit solutions for specific applications like asset liquidation and real options valuation.

Contribution

It constructs an explicit optimal equilibrium under certain conditions and establishes criteria for its uniqueness in time-inconsistent stopping problems.

Findings

Explicit formulas for optimal equilibria in three stopping problems

Conditions for the uniqueness of optimal equilibria

Comprehensive analysis of asset liquidation and real options valuation

Abstract

For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub-additive and the state process is one-dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and integrability conditions. While there may exist other optimal equilibria, we show that they can differ from the constructed one in very limited ways. This leads to a sufficient condition for the uniqueness of optimal equilibria, up to some closedness condition. To illustrate our theoretic results, comprehensive analysis is carried out for three specific stopping problems, concerning asset liquidation and real options valuation. For each one of them, an optimal equilibrium is characterized through an explicit formula.