Optimal Switching over Multiple Regimes

This paper studies the optimal switching problem for a general one-dimensional diffusion with multiple (more than two) regimes. This is motivated in the real options literature by the investment problem of a firm managing several production modes while facing uncertainties. A viscosity solutions approach is employed to carry out a fine analysis on the associated system of variational inequalities, leading to sharp qualitative characterizations of the switching regions. These characterizations, in turn, reduce the switching problem into one of finding a finite number of threshold values in state that would trigger switchings. The results of our analysis take several qualitatively different forms depending on model parameters, and the issue of when and where it is optimal to switch is addressed. The general results are then demonstrated by the threeregime case, where a quasi-explicit solution is obtained, and a numerical procedure to find these critical values is devised in terms of the expectation functionals of hitting times for one-dimensional diffusions.