论文标题
一维扩散过程的时间不一致的平衡
Equilibria of Time-inconsistent Stopping for One-dimensional Diffusion Processes
论文作者
论文摘要
我们考虑文献中提出的三个平衡概念，以解决时间不一致的问题，包括轻度平衡，弱平衡和强烈的平衡。假定折扣功能是对数次加addive的，并且基础过程是一维扩散。我们首先为表征弱平衡提供了必要和充分的条件。平滑拟合条件作为副产品获得。接下来，基于弱平衡的特征，我们表明最佳的轻度平衡也很弱。然后，我们提供弱平衡强度的条件。我们进一步表明，在一定条件下，最佳的轻度平衡也很强。最后，我们提供了几个示例，其中包括一个示例，表明弱平衡可能并不强，并且另一个表明强烈的平衡可能不是最佳的温和。
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the underlying process is one-dimensional diffusion. We first provide necessary and sufficient conditions for the characterization of weak equilibria. The smooth-fit condition is obtained as a by-product. Next, based on the characterization of weak equilibria, we show that an optimal mild equilibrium is also weak. Then we provide conditions under which a weak equilibrium is strong. We further show that an optimal mild equilibrium is also strong under a certain condition. Finally, we provide several examples including one shows a weak equilibrium may not be strong, and another one shows a strong equilibrium may not be optimal mild.
