Lecture Summer Term 2017

Lévy Processes


Alexander Lindner
Class Teacher:
Dirk Brandes

MSc. Finance: Elective course in Financial Mathematics or Stochastic

MSc. Mathematics/WiMa: Elective course in Financial Mathematics

2+1 SWS, 4 CP


On Monday, 3rd of July, the lecture is cancelled.

On Monday, 24th of April, is given an additionally lecture from 14 to 16 pm in He18 - 2.20.

Time and Venue:Schedule of the course:
  • Lecture: Monday, 8:00-10:00, He18 - 2.20
  • First Lecture: 24/04/2017
  • Exercise classMonday, 14:00-16:00, He18 - 2.20, every two weeks.
  • First Exercise class: 08/05/2017

Final Exam:

oral (no prerequisites)


Measure Theoretic Probability and some basic knowledge about stochastic processes (Brownian Motion, Poisson Process).


This course covers the basic and advanced theory of Lévy Processes including:

  • Infinitely Divisible Distributions
  • The Lévy-Khintchine formula
  • The Characteristic Triplet.
  • Existence of Lévy Processes
  • Moments of Lévy Processes
  • Stable Processes and Stable Lévy Processes
  • The Lévy-Itô-Decomposition and Applications


A list of reference books would cover the following works:
  • K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge, 2nd edition, 2014.
  • D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge, 2nd edition, 2009.
  • A. E. Kyprianou, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Springer, 2006.

Exercise sheets:


Lecture notes: