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UNIVAQ RANDOM TALKS 

Online talks on Probability and Applications at
DISIM -  UNIVERSITÁ DI L'AQUILA 

Using  Zoom Videoconference system
Monday 18th 2:30 p.m.
Prof. Giorgio Ferrari - Bielefeld University

TITLE: Singular Control of the Drift of a Brownian System

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ABSTRACT: 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 with interconnected dynamics 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. The optimal control is also constructed (weakly) under further specifications of the model. This talk is based on a joint work with Salvatore Federico (University of Siena) and Patrick Schuhmann (Bielefeld University).

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Fabio Antonelli
DISIM - Università di L'Aquila