2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72857This 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.ProbabilityMSC: 60G40, 49L25, 60H30text