Seminario Dottorato: “On a Particular Class of Singular Optimal Control Problems”

Wednesday 27 June 2018, h. 15:00 - Room 2BC30 - Torben Koch

ARGOMENTI: Seminars Ph.D. Program

Wednesday 27 June 2018, h.15:00, Room 2BC30
Torben Koch (Bielefeld University, Center for Mathematical Economics)
“On a Particular Class of Singular Optimal Control Problems”

Optimal control problems have been attracted by many researchers in recent years. Its applications can be found in different fields of sciences such as physics or economics. In this talk, we study a particular class of singular optimal control problems, that is, the control variable is represented by an increasing and right-continuous process. Therefore the control measure is allowed to be singular with respect to the Lebesgue measure. The optimal control and value of the problem are typically characterized by a partial differential equation, the so-called Hamilton-Jacobi-Bellman (HJB) equation. In a first step we study a deterministic setting in which the controlled system is governed by an ordinary differential equation. We derive the associated HJB equation by employing standard techniques such as Taylor's theorem. In a next step, we extend the model and consider a specific stochastic singular control problem. The model we have in mind is that of a firm which aims to maximize its profits from selling energy in the market. Here, the control variable represents the firm's installation strategy of solar panels in order to produce energy. We assume that the energy price follows an Ornstein-Uhlenbeck process and is affected by the installation strategy of the firm. We find that the optimal installation strategy is triggered by a threshold, the so-called free boundary which separates the waiting region, in which it is not optimal to install additional panels, and the installation region where it is optimal to install additional panels. Finally, our study is complemented by an analysis of the dependency of the optimal installation strategy on the model's parameters.

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