Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems
Mathematical Finance
2021-07-14 v3 Optimization and Control
Probability
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.
Keywords
Cite
@article{arxiv.2006.00754,
title = {Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems},
author = {Yu-Jui Huang and Zhenhua Wang},
journal= {arXiv preprint arXiv:2006.00754},
year = {2021}
}