论文标题
一般最佳停止线性成本
General Optimal Stopping with Linear Costs
论文作者
论文摘要
本文将离散的时间和连续的时间与一般线性成本在真实线上的一般过程中停止问题。使用最大表示类型的辅助函数，提供条件，以确保最佳的停止时间为阈值类型。然后将最佳阈值表征为该函数的根。对于随机行走，我们的结果凝结了一个事实，即凹入的所有收益功能和凸成本功能的所有组合都会导致单方面解决方案。对于Lévy过程，获得辅助功能的明确方法，并且通过使用梯子高度过程给出阈值。最后，讨论了从离散和连续问题以及后一个通过前一个问题的近似的联系。
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to guarantee the optimal stopping time to be of threshold type. The optimal threshold is then characterized as the root of that function. For random walks our results condense in the fact that all combinations of concave increasing pay-off functions and convex cost functions lead to a one-sided solution. For Lévy processes an explicit way to obtain the auxiliary function and the threshold is given by use of the ladder height processes. Lastly, the connection from discrete and continuous problem and possible approximation of the latter one via the former one is discussed.
