On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems
On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems
复制标题
关于寻找时间不一致马尔可夫问题的平衡停止时间
DOI：
10.1137/17m1153029
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Kristoffer Lindensjö
中科院分区：
文献类型：
--
作者：
S. Christensen;Kristoffer Lindensjö
标准马尔可夫最优停止问题是一致的，因为第一次进入停止集的时间对于过程的每个初始状态都是最佳的。显然，如果没有这种时间一致的结构，通常的最优性概念就不能以直接的方式应用于非标准停止问题。本文致力于使用博弈论方法来解决时间不一致的停止问题，其中奖励取决于初始状态，其中过程的每个状态对应于游戏中的玩家。更准确地说，我们给出了精确的均衡定义——基于纯马尔可夫策略的子博弈完美纳什均衡。这种平衡并不总是存在。然而，我们开发了一种迭代方法来寻找一类一般问题的平衡停止时间，并将这种方法应用于实线上的单边停止问题。我们还证明了基于一组变分不等式的验证定理，这也使我们能够找到均衡。作为已发展理论的应用，我们研究指数效用和内生习惯形成下的销售策略问题。
Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a straightforward way be applied to non-standard stopping problems without this time-consistent structure. This paper is devoted to the solution of time-inconsistent stopping problems with the reward depending on the initial state using a game-theoretic approach in which each state of the process corresponds to a player in the game. More precisely, we give a precise equilibrium definition - of the type subgame perfect Nash equilibrium based on pure Markov strategies. Such equilibria do not always exist. We, however, develop an iterative approach to finding such equilibrium stopping times for a general class of problems and apply this approach to one-sided stopping problems on the real line. We furthermore prove a verification theorem based on a set of variational inequalities which also allows us to find equilibria. As an application of the developed theory we study a selling strategy problem under exponential utility and endogenous habit formation.
影响因子：
1.7
作者：
Yu‐Jui Huang;Adrien Nguyen Huu
通讯作者：
Yu‐Jui Huang;Adrien Nguyen Huu