Optimal Equilibria for Multidimensional Time-Inconsistent Stopping Problems
Yu-Jui Huang, Zhenhua Wang · SIAM Journal on Control and Optimization · 2021
We study an optimal stopping problem under nonexponential discounting, where the state process is a multidimensional continuous strong Markov process. The discount function is taken to be log subadditive, capturing decreasing impatience 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.