Probability Seminar - Leo Neufcourt

Institution: Michigan State University
Title: Expansions of Filtrations and Information Drift
Date: Thursday, November 16, 2017
Location: C405 Wells Hall
Time: 3:00 PM - 3:50 PM

Expansions of filtrations induce a fundamental change in semimartingales - which recover all stochastic processes considered in practice. Non degeneracy conditions require the conservation of the semimartingale property as well as the apparition of an information drift, which integrates into an additional finite variation term in the semimartingale decomposition and characterizes the change in the prediction of the dynamics of the semimartingale associated with the expansion.

We will focus on expansions of filtrations generated by a stochastic process and propose a method to estimate the information drift based on a discretization of the process, convergence of filtrations and extensions of measures. We will also study a family of examples inspired by an application to evaluating the advantage of high-frequency trading.