论文标题
停止未知状态的问题
Stopping problems with an unknown state
论文作者
论文摘要
我们在完整信息下扩展了最佳停止问题的经典设置，以包括未知状态的问题。该框架允许未知状态影响（i）基础过程的漂移，（ii）收益功能以及（iii）时间范围的分布。由于假定塞子可以观察到基本过程和随机范围，因此这是一个两源的学习问题。为未知状态分配先前的分布，过滤理论可以用来将问题嵌入马尔可夫框架中，因此我们将问题不完整的信息减少到具有完整信息的问题，但使用了更多的状态变量。我们基于一种量度变化技术，提供了简化的问题的公式，该技术将基本过程与代表未知状态后验的状态变量分解。此外，我们通过几个新示例表明，这种减少的配方可用于明确解决问题。
We extend the classical setting of an optimal stopping problem under full information to include for problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, filtering theory can be used to embed the problem in a Markovian framework, and we thus reduce the problem with incomplete information to a problem with complete information but with one more state-variable. We provide a convenient formulation of the reduced problem, based on a measure change technique that decouples the underlying process from the state variable representing the posterior of the unknown state. Moreover, we show by means of several new examples that this reduced formulation can be used to solve problems explicitly.
