SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1705-1729, January 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.

中文翻译：

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多维时间不一致停止问题的最佳平衡

SIAM控制与优化杂志，第59卷，第2期，第1705-1729页，2021年1月。
我们研究非指数贴现下的最优停止问题，其中状态过程是多维连续的强马尔可夫过程。折现函数被认为是对数次加法，捕获了行为经济学中越来越少的急躁情绪。在概率势理论的基础上，我们建立了一个足够大的均衡集合之间的最优均衡，该均衡集合由满足边界条件的精细封闭均衡组成。这概括了现有文献中针对一维停止问题的最佳平衡的存在。