Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems

Abstract

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience in behavioral economics. On 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.

References in corpus (4)

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• On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems
• The Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case
• Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

Cited by in corpus (3)

• Weak equilibria for time-inconsistent control: with applications to investment-withdrawal decisions
• A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria
• Partial Information in a Mean-Variance Portfolio Selection Game