Singular Control of the Drift of a Brownian System

Federico S, Ferrari G, Schuhmann P (2020) Center for Mathematical Economics Working Papers; 637.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.

MSC2010 subject classification: 93E20, 91A55, 49L25, 49J40, 35R35, 91B64
Stichworte
singular stochastic control; Dynkin game; viscosity solution; free boundary; smooth-fit; Brownian motion; ordinary differential equation
Erscheinungsjahr
2020
Band
637
Seite(n)
22
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2943686

Zitieren

Federico S, Ferrari G, Schuhmann P. Singular Control of the Drift of a Brownian System. Center for Mathematical Economics Working Papers. Vol 637. Bielefeld: Center for Mathematical Economics; 2020.
Federico, S., Ferrari, G., & Schuhmann, P. (2020). Singular Control of the Drift of a Brownian System (Center for Mathematical Economics Working Papers, 637). Bielefeld: Center for Mathematical Economics.
Federico, S., Ferrari, G., and Schuhmann, P. (2020). Singular Control of the Drift of a Brownian System. Center for Mathematical Economics Working Papers, 637, Bielefeld: Center for Mathematical Economics.
Federico, S., Ferrari, G., & Schuhmann, P., 2020. Singular Control of the Drift of a Brownian System, Center for Mathematical Economics Working Papers, no.637, Bielefeld: Center for Mathematical Economics.
S. Federico, G. Ferrari, and P. Schuhmann, Singular Control of the Drift of a Brownian System, Center for Mathematical Economics Working Papers, vol. 637, Bielefeld: Center for Mathematical Economics, 2020.
Federico, S., Ferrari, G., Schuhmann, P.: Singular Control of the Drift of a Brownian System. Center for Mathematical Economics Working Papers, 637. Center for Mathematical Economics, Bielefeld (2020).
Federico, Salvatore, Ferrari, Giorgio, and Schuhmann, Patrick. Singular Control of the Drift of a Brownian System. Bielefeld: Center for Mathematical Economics, 2020. Center for Mathematical Economics Working Papers. 637.
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