Singular control and impulse control : A common approach

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

7 Scopus Citations
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)27-57
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series B
Volume13
Issue number1
Publication statusPublished - Jan 2010
Externally publishedYes

Abstract

In this study, we investigate the connection between impulse control and singular control. The dynamic systems are driven by Brownian motion with drift. For simplicity we consider only one-dimension problems, where we can perform explicit calculations. We will see that Quasi-Variational Inequalities (QVI) are the common tool to consider these problems. The two problems have interesting links. By some aspects, singular control problems appear as particular cases of impulse control problems; however an impulse control is a particular case of singular control. We can, in particular, approximate an optimal singular control by a minimizing sequence of impulse controls. We show that optimal singular controls are linked to reflected diffusions. Thanks to the one-dimensionality we completely solve the QVI by the two band approach.

Research Area(s)

  • Impulse control, Quasi-variational inequalities, Reflected diffusion, Singular control