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Singular Control of the Drift of a Brownian System

Salvatore Federico, Giorgio Ferrari and Patrick Schuhmann
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Salvatore Federico: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Patrick Schuhmann: Center for Mathematical Economics, Bielefeld University

No 637, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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 di fferentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary diff erential equations.

Keywords: singular stochastic control; Dynkin game; viscosity solution; free boundary; smooth-fit; Brownian motion; ordinary differential equation (search for similar items in EconPapers)
Pages: 22
Date: 2020-05-29
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https://pub.uni-bielefeld.de/download/2943686/2943687 First Version, 2020 (application/pdf)

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