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摘要翻译：
对于离散时间马尔可夫链，根据Strotz的一致规划，我们建立了一个考虑期望报酬非线性函数的时间不一致的最优停止问题的框架。我们考虑纯停止策略和混合停止策略以及一个（子博弈完美纳什）均衡。我们给出了不同的充要条件，包括一个验证定理。利用一个不动点论元，我们给出了平衡点存在性的结果。我们适应和研究了近视调整过程的概念，并介绍了不同类型的平衡稳定性。我们证明平衡点的存在性和唯一性一般都不应被期望。将发展的理论应用于一个均值-方差问题和一个方差问题。
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英文标题：
《Time-inconsistent stopping, myopic adjustment & equilibrium stability:
with a mean-variance application》
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作者：
S\"oren Christensen and Kristoffer Lindensj\"o
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最新提交年份：
2020
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We consider pure and mixed stopping strategies and a (subgame perfect Nash) equilibrium. We provide different necessary and sufficient equilibrium conditions including a verification theorem. Using a fixed point argument we provide equilibrium existence results. We adapt and study the notion of the myopic adjustment process and introduce different kinds of equilibrium stability. We show that neither existence nor uniqueness of equilibria should generally be expected. The developed theory is applied to a mean-variance problem and a variance problem.
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PDF链接：
https://arxiv.org/pdf/1909.11921
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