Explicit Solution to an Optimal Switching Problem in the Two‐Regime Case

This paper considers the problem of determining the optimal sequence of stopping times for a diffusion process subject to regime switching decisions. This is motivated in the economics literature by the investment problem under uncertainty for a multi‐activity firm involving opening and closing decisions. We use a viscosity solutions approach combined with the smooth‐fit property, and explicitly solve the problem in the two‐regime case when the state process is of geometric Brownian nature. The results of our analysis take several qualitatively different forms, depending on model parameter values.