EMS School on Stochastic Analysis


Prof. Frank den Hollander, Universiteit Leiden
"Random Walk in Dynamic Random Environment" (Abstract)


1) Background and motivation

2) Main results achieved so far

3) Main open problems

4) Basic technique 1: Regeneration

5) Basic technioque 2: Renormalisation


Dr Jan Obloj, University of Oxford
"On aspects of the Skorokhod embedding problem and its applications"


1) Classical vs Robust Modelling Framework in Mathematical Finance

2) Time-changing toolbox

2.1 Stopping times and their properties, small stopping times

2.2 Changes of time

2.3 Elements of potential theory, first-hitting times

3) On some solutions to the Skorokhod embedding problem and their properties

4) Root's solution, links with PDEs and time-reversal

5) On some n-marginal problems and resulting martingale inequalities

The two courses will mostly takle place in the morning with a lecture of 60 to 90 minutes each. Several afternoons are reserved for presentations by the students to present their projects and their work to date.