Admission requirements
This is a Master level course, basic knowledge of probability theory (IKR) and measure theory is required.
Description
The first part of this course discusses the Cramer-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
The objective of the course is to expose the students into the introductory concepts of ruin theory and also rare events, through extreme values. Also learn about what are the basic models.
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
Classroom lectures. One day per week (90 minutes). There will be no exercise classes, but there might be office hours to discuss the doubts.
Assessment method
The exam will be written/ oral.
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: Sidney Resnick
Modelling extremal events: Paul Embrechts, Claudia Kluppelberg 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
Rajat Hazra (r.s.hazra@math.leidenuniv.nl)
Michel Mandjes ( m.r.h.mandjes@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.