Date: Wednesday, February 02, 2022
Location: Zoom Virtual (4:00 PM to 5:00 PM)
Title: Learning to reflect  Datadriven solutions to singular control problems
Abstract: Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their practicability suffers from the assumption of known dynamics of the underlying stochastic process, raising the statistical challenge of developing purely datadriven controls in a nonparametric framework.
In this talk, we will mainly concentrate on longterm average singular control problems for general Lévy processes on the real line. First, we present a method for solving such problems for known underlying dynamics in terms of the ladder height process. To construct a datadriven procedure, the fundamental observation is that this solution can be represented using an auxiliary function involving the stationary distribution of the overshoot process. This leads to the statistical question of finding rateoptimal estimators with respect to the supnorm risk for such functionals. As a result, we present a fully datadriven strategy that is optimal on the long run and show that the regret per time unit is of order $1/\sqrt(T)$.
Files: 7639_michigan2022.pdf
Speaker: Soren Christensen
Institution: ChristianAlbrechtsUniversity Kiel
Event Organizer: Erhan Bayraktar
