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Titel
Singular control of the drift of a Brownian system / Salavatore Federico, Giorgio Ferrari, and Patrick Schuhmann
VerfasserFederico, Salvatore ; Ferrari, Giorgio ; Schuhmann, Patrick
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, May 2020
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Elektronische Ressource
Umfang1 Online-Ressource (21 Seiten) : Illustrationen
SerieCenter for Mathematical Economics Working papers ; 637
SchlagwörterStochastik / Brownsche Bewegung / Differentialgleichung
URNurn:nbn:de:hbz:6:2-1426894 
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Singular control of the drift of a Brownian system [0.48 mb]
Zusammenfassung

We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem's value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously differentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary differential equations.

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