论文标题
停止尖峰，延续托架和其他特征的最佳停止，并有限时间范围
Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon
论文作者
论文摘要
我们考虑使用有限的时间范围和州依赖性折扣的最佳停止问题。基础过程是一维线性扩散，增益函数是时间均匀的，并且两个凸功能的差异。在具有局部性质的轻度技术假设下，我们证明了最佳停止边界的良好规律性特性，包括其连续性和严格的单调性。后者从来没有得到概率论点的证明。我们还表明，与增益函数的二阶空间导数相关的签名度量中的原子会诱导延续/停止集的几何特性，而持续/停止集的几何特性则无法通过平滑的增益函数观察到（我们称它们为\ emph {continuation bays} and \ emph {stop spikes}）。值函数在时间上是不断差异的，而无需对增益函数的平滑度进行任何要求。
We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion and the gain function is time-homogeneous and difference of two convex functions. Under mild technical assumptions with local nature we prove fine regularity properties of the optimal stopping boundary including its continuity and strict monotonicity. The latter was never proven with probabilistic arguments. We also show that atoms in the signed measure associated with the second order spatial derivative of the gain function induce geometric properties of the continuation/stopping set that cannot be observed with smoother gain functions (we call them \emph{continuation bays} and \emph{stopping spikes}). The value function is continuously differentiable in time without any requirement on the smoothness of the gain function.
