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)