On the smooth-fit property for one-dimensional optimal switching problem

This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of variational inequa-lities, and the state space is divided into continuation regions and switching regions. By means of viscosity solutions approach, we prove the smoot-fit $C^1$ property of the value functions