Probability, statistics and combinatorics: Bayesian sequential least-squares estimation for the drift of a Wiener process

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Erik Ekström
  • Contact person: Fiona Skerman
  • Seminarium

Abstract: Given a Wiener process with unknown and unobservable drift, we seek to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a linearly growing cost for the observation duration. In a Bayesian framework, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale; we provide structural properties of the solution for the corresponding problem of optimal stopping. This is joint work with Ioannis Karatzas and Juozas Vaicenavicius.