Some results on optimal stopping problems for one-dimensional regular diffusions

Dongchao Huang, Jian Song

Published 2017-07-09Version 1

For a type of employee stock option (ESO) and American put options with a barrier, we obtain closed-form formulae for the value functions and provide a complete characterization for optimal stopping/continuation regions. Some comparison principles for the critical levels and value functions are also given. This work is inspired by the characterization of the value functions for general one-dimensional regular diffusion processes developed in \cite{DK03} by Dayanik and Karatzas.