Singular control of the drift of a Brownian system - Salavatore Federico; Giorgio Ferrari; Patrick Schuhmann (Bielefeld University, Center for Mathematical Economics (IMW), 2020)
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 differentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary differential equations.
urn:nbn:de:0070-pub-29436868
Keywords: 330; singular stochastic control; Dynkin game; viscosity solution; free boundary; smooth-t; Brownian motion; ordinary differential equation