论文标题
旧问题，经典方法，新解决方案
Old Problems, Classical Methods, New Solutions
论文作者
论文摘要
我们使用本文作者及其合作者最近开发的经典热能方法的强大扩展来解决金融数学的几个重大问题。我们详细考虑以下问题：（a）将结构默认框架中的默认边界校准为恒定的默认强度； （b）在平均场框架中计算代表银行的默认概率； （c）找到Ornstein-uhlenbeck过程的打击时间概率密度。通过其他几个问题，包括American Put Option和寻找最佳的均值交易策略。此外，还简要讨论了两个非财务应用程序 - 超冷的Stefan问题和集成和开火神经科学问题。
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in detail: (A) calibrating the default boundary in the structural default framework to a constant default intensity; (B) calculating default probability for a representative bank in the mean-field framework; (C) finding the hitting time probability density of an Ornstein-Uhlenbeck process. Several other problems, including pricing American put options and finding optimal mean-reverting trading strategies, are mentioned in passing. Besides, two non-financial applications -- the supercooled Stefan problem and the integrate-and-fire neuroscience problem -- are briefly discussed as well.
