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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

Everybody is welcome, please subscribe by the following form The day of the seminar, participants will receive an invitation by e-mail [https://lh5.googleusercontent.com/CWhLsT4lqNWzIjVe3mEN_7Iq4wxE9g204khy6mYxfL...]https://docs.google.com/forms/d/e/1FAIpQLSclukp_QZeujS15nbL3IvtRKGJWvHkx-E5fYbDH9zG3O5QvWg/closedform UNIVAQ RANDOM TALKS 3 - UNIVERSITÁ DI L'AQUILAhttps://docs.google.com/forms/d/e/1FAIpQLSclukp_QZeujS15nbL3IvtRKGJWvHkx-E5fYbDH9zG3O5QvWg/closedform ONLINE May 18th 2020 - 2:30 p.m. Prof. Giorgio Ferrari - Bielefeld University: Singular Control of the Drift of a Brownian System docs.google.com No need to subscribe, if, in a previous form, you asked to be always included

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