Singular Control of the Drift of a Brownian System

Federico S, Ferrari G, Schuhmann P (2021)
Applied Mathematics & Optimization.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | 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 has interconnected dynamics and it 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.
Stichworte
Singular stochastic control; Dynkin game; Viscosity solution; Free; boundary; Smooth-fit; Brownian motion; Ordinary differential equation
Erscheinungsjahr
2021
Zeitschriftentitel
Applied Mathematics & Optimization
ISSN
0095-4616
eISSN
1432-0606
Page URI
https://pub.uni-bielefeld.de/record/2955114

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Federico S, Ferrari G, Schuhmann P. Singular Control of the Drift of a Brownian System. Applied Mathematics & Optimization. 2021.
Federico, S., Ferrari, G., & Schuhmann, P. (2021). Singular Control of the Drift of a Brownian System. Applied Mathematics & Optimization. https://doi.org/10.1007/s00245-021-09779-3
Federico, S., Ferrari, G., and Schuhmann, P. (2021). Singular Control of the Drift of a Brownian System. Applied Mathematics & Optimization.
Federico, S., Ferrari, G., & Schuhmann, P., 2021. Singular Control of the Drift of a Brownian System. Applied Mathematics & Optimization.
S. Federico, G. Ferrari, and P. Schuhmann, “Singular Control of the Drift of a Brownian System”, Applied Mathematics & Optimization, 2021.
Federico, S., Ferrari, G., Schuhmann, P.: Singular Control of the Drift of a Brownian System. Applied Mathematics & Optimization. (2021).
Federico, Salvatore, Ferrari, Giorgio, and Schuhmann, Patrick. “Singular Control of the Drift of a Brownian System”. Applied Mathematics & Optimization (2021).

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