Lévy Processes

MSc Finance: Elective Course in Financial Mathematics or Stochastics

MSc Mathematics/Wima: Elective Course in Financial Mathematics

2+1 SWS lecture + exercise; 4 credit points

Time and Venue:

Lectures: Monday 12.15-14, He220;

First lecture: 12/10/2015;

Exercises: Tuesday 16.15-18, N24 - 131;

First exercise class: 20/10/2015;

Measure theoretic probability and basic knowledge of stochastic processes (Brownian motion, Poisson process)

Infinitely divisible distributions
The Lévy-Khintchine formula
Existence of Lévy processes
Moments of Lévy processes
Stable distributions and stable Lévy processes
The Lévy-Itô-decomposition and applications

Exam:

oral (no prerequisites)

Lecture notes will be made available. Additionally please consult:

Sato, Ken-iti (2014): Lévy processes and infinitely divisible distributions. Cambridge, 2nd edition.

Applebaum, D. (2009) Lévy processes and stochastic calculus. Cambridge, 2nd edition.

Kyprianou, Andreas E. (2006): Introductory lectures on fluctuations of Lévy processes with applications. Springer.