Singular control of the drift of a Brownian system
A talk in the Keine Reihe series by
Patrick Schuhmann
| Abstract: | We consider a standard Brownian motion whose drift can be increased or decreased in a possiblysingular manner. The objective is to minimize an expected functional involving the time-integral ofa running cost and the proportional costs of adjusting the drift. The resulting two-dimensionaldegenerate singular stochastic control problem is solved by combining techniques of viscositytheory and free boundary problems. We provide a detailed description of the problem's valuefunction and of the geometry of the state space, which is split into three regions by two monotonecurves. Our main result shows that those curves are continuously differentiable with locallyLipschitz derivative and solve a system of nonlinear ordinary differential equations.
This talk takes place within the retreat of the CRC 1283. All members of the CRC are invited to attend. Please contact ckoehler@math.uni-bielefeld.de for Zoom-Link, Meeting-ID and Password.
|