Smooth fit principle for impulse control of multidimensional diffusion processes. (English) Zbl 1194.49016
Summary: Value functions of impulse control problems are known to satisfy Quasi-Variational Inequalities (QVIs) [A. Bensoussan and J.-L. Lions, Methodes Mathematiques de l’Informatique, 11. Publie avec le concours du C.N.R.S. Paris: Dunod. XV, 596 p. (1982; Zbl 0491.93002)]. This paper proves the smooth-fit \(C^1\) property of the value function for multidimensional controlled diffusions, using a viscosity solution approach. We show by examples how to exploit this regularity property to derive explicitly an optimal policy and value functions.
MSC:
49J40 | Variational inequalities |
49N25 | Impulsive optimal control problems |
49N60 | Regularity of solutions in optimal control |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
49J55 | Existence of optimal solutions to problems involving randomness |