论文标题
一类带有最佳停止及其倒数问题的平均场游戏
A Class of Mean-Field Games with Optimal Stopping and its Inverse Problem
论文作者
论文摘要
本文重新研究了经过充分研究的\ emph {最佳停止}问题，但在\ emph {大填充}框架内。特别是，通过考虑\ emph {相对性能标准}来提出两类最佳停止问题。相对绩效标准非常引人注目，也是由\ emph {joness偏爱}，\ emph {习惯形成实用程序}或\ emph {相对财富关注}在经济学和金融中的\ emph {相对财富关注}，在解释各种决策行为（例如价格泡泡）方面起着重要作用。通过在大型人口环境中引入此类标准，给定代理可以将其单独的停止规则与其同类的平均行为进行比较。为了得出分散的停止规则，制定了相关的平均场游戏。相关的一致性条件是通过一些耦合方程系统来表征的，并且还验证了渐近nash平衡特性。另外，还引入和讨论了一些\ emph {逆}均值最佳停止问题。
This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative performance criteria}. It is remarkable the relative performance criteria, also understood by the \emph{Joneses preference}, \emph{habit formation utility}, or \emph{relative wealth concern} in economics and finance, plays an important role in explaining various decision behaviors such as price bubbles. By introducing such criteria in large-population setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated mean-field games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the asymptotic Nash equilibrium properties are also verified. In addition, some \emph{inverse} mean-field optimal stopping problem is also introduced and discussed.
