Explicit solution to an optimal switching problem in the two regimes case

Huyen Pham (1) , Vathana Ly Vath (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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, and explicitly solve the problem in the two regimes case when the state process is of geometric Brownian nature.

Keywords: Optimal switching; system of variational inequalities; viscosity solutions; smooth-fit principle.; smooth-fit principle

Domains: Probability [math.PR]

Huyen Pham, Vathana Ly Vath. Explicit solution to an optimal switching problem in the two regimes case. 2005. ⟨hal-00008125⟩