A class of solvable impulse control problems
Easily verifiable sufficient conditions for explicit solvability of an impulse control problem with a linear, regular, and time-homogeneous diffusion as underlying dynamics are derived. An algebraic equation for the optimal impulse boundary is given, and the value of the optimal impulse boundary is determined in terms of the minimal increasing \(r\)-excessive mapping for the diffusion. The results are illustrated in the case of an underlying geometric Brownian motion.
scientific article; zbMATH DE number 2111584