英文标题：
《Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in
Continuous Time》
---
作者：
Yu-Jui Huang and Zhou Zhou
---
最新提交年份：
2019
---
英文摘要：
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms \"strong equilibria\" and \"weak equilibria\" are coined for controls under the new and the standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to Kakutani-Fan\'s fixed-point theorem, general existence of weak and strong equilibria is also established, under additional compactness assumption. Our theoretic results are applied to a two-state model under non-exponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.
---
中文摘要：
引入了连续时间平衡控制的新定义。与涉及衍生类型操作的标准定义不同，新定义与离散时间均衡的定义类似，并允许明确的经济解释。术语“强平衡”和“弱平衡”分别是在新定义和标准定义下为控制创造的。当状态过程是时间齐次连续时间马尔可夫链时，仔细的渐近分析给出了弱平衡点和强平衡点的完整刻画。借助Kakutani-Fan的不动点定理，在附加紧性假设下，还建立了弱平衡点和强平衡点的一般存在性。我们的理论结果被应用于非指数贴现下的两态模型。特别是，我们明确证明，可能存在偏离弱均衡的动机，这证明需要强均衡。我们的分析也为无限视界下离散时间平衡的存在性和特征提供了新的结果。
---
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
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->