6 ECTS credits
150 h study time

Offer 1 with catalog number 4015703FNR for all students in the 2nd semester at a (F) Master - specialised level.

Semester
2nd semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Registration for "Levy Processes and their Applications" is allowed if one is registered for or has succesfully accomplished "Advanced Probability".
Taught in
Dutch
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Uwe Einmahl (course titular)
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content
First  the general theory of  the structure of the Levy processes is studied. Then we consider a number of important statements:
-The Levy-Khintchine formula;
- The Levy-Ito decomposition.
Further, we deal with the Markov property of Levy processes and its practcal implications. In the sequel we
consider the exponential martingales that  are useful  for deriving the Laplace transforms of the "first passage time" problem. The practical applications of the mentioned topics are discussed.
Finally, we deal with the Wiener-Hopf factorization which serves as a very handy tool for solving boundary problems for Levy processes.
Course material
Digital course material (Required) : Lévy processen en hun toepassingen, De nota's van docent.
Handbook (Recommended) : Levy processes in Finance: pricing financial derivatives, Pricing financial derivatives, W. Schoutens, Wiley, 9780470851562, 2003
Digital course material (Recommended) : Introductory Lectures on Fluctuations of Levy Processes with Applications, Kyprianou A., http://www.springer.com/la/book/9783642376313, 9783642376320, 2006
Practical course material (Required) : Artiekelen die zullen uitgedeeld worden.
Additional info

none

Learning Outcomes

General competencies

Student has basic knowledge over the structure of Levy processes. The student can work with articles and books on individual basis; thinks and analyzes  critically.  The student knows some areas of applications of Levy processes. The student is able to start a master thesis in this area.

Grading

The final grade is composed based on the following categories:
Written Exam determines 40% of the final mark.
SELF Presentation determines 60% of the final mark.

Within the Written Exam category, the following assignments need to be completed:

  • schriftelijk examen with a relative weight of 1 which comprises 40% of the final mark.

    Note: Het schriftelijke (40 %) examen

Within the SELF Presentation category, the following assignments need to be completed:

  • individuele project with a relative weight of 1 which comprises 60% of the final mark.

Additional info regarding evaluation

none

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Financial and Applied Mathematics (only offered in Dutch)
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)