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Title: Singular control and impulse control : a common approach
Authors: Bensoussan, A
Yuan, J
Keywords: Impulse control
Quasi-variational inequalities
Reflected diffusion
Singular control
Issue Date: 2010
Publisher: AIMS
Source: Journal of dscrete and continuous dynamical system, 2010, v. 13, no. 1, p. 27-57 How to cite?
Journal: Journal of dscrete and continuous dynamical system
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.
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2010.13.27
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