TY  - GEN
AB  - 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.
DA  - 2020
KW  - singular stochastic control
KW  - Dynkin game
KW  - viscosity solution
KW  - free boundary
KW  - smooth-fit
KW  - Brownian motion
KW  - ordinary differential equation
LA  - eng
PY  - 2020
SN  - 0931-6558
SP  - 22-
TI  - Singular Control of the Drift of a Brownian System
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29436868
Y2  - 2024-11-24T18:43:03
ER  -