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