Admission requirements
Basic knowledge of probability theory (IKR) and measure theory is required.
Description
The first part of this course discusses the Cramér-Lundberg model, being the cornerstone model in insurance mathematics and ruin theory, and various of its generalizations. In the approach followed, an explicit connection with associated queueing models is made. A wealth of probabilistic techniques is used, including transform methods, martingales, large deviations and change-of-measure.
The second part of this course concerns extreme value theory, which originated from an interest in examining the behavior of maximum or minimum values of independent and identically distributed (i.i.d.) random variables. Over time, extreme value theory has found applications in diverse fields such as finance, risk management, telecommunications, environmental studies, and pollution research. The analysis is structured into three main parts: an introduction to univariate extreme value theory, multivariate extreme value theory, and point process techniques with applications to extreme value theory.
Course Objectives
After completion of the course, the student is familiar with the fundamental concepts of ruin theory and extreme value theory. The student will understand and be able to apply the key models used in these areas.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
Lectures (90 minutes/week) and homework on a regular basis.
Assessment method
Homework (40% of final grade) and final oral exam (60% of final grade). In order to pass the course the grade for the oral exam needs to be at least 5, and the weighted average of homework and oral exam needs to be at least 5.5. No minimum grade for the homework is required in order to be allowed for the exam or in order to pass the course. The homework counts as a practical and there is no retake for it.
Reading list
The Cramér-Lundberg Model and Its Variants: a queueing perspective by Michel Mandjes and Onno Boxma
Extremes Values, Regular Variation and Point Processes by Sidney Resnick
Modelling Extremal Events by Paul Embrechts, Claudia Klüppelberg and Thomas Mikosch
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
Michel Mandjes ( m.r.h.mandjes@math.leidenuniv.nl)
Moritz Otto (m.f.p.otto@math.leidenuniv.nl)
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.