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.

Singular Control of the Drift of a Brownian System / Federico S.; Ferrari G.; Schuhmann P.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 84:Suppl 1(2021), pp. 561-590. [10.1007/s00245-021-09779-3]

Singular Control of the Drift of a Brownian System

Federico S.;
2021

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 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.
2021
Singular Control of the Drift of a Brownian System / Federico S.; Ferrari G.; Schuhmann P.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 84:Suppl 1(2021), pp. 561-590. [10.1007/s00245-021-09779-3]
Federico S.; Ferrari G.; Schuhmann P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/944378
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