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Ruin Theory and Extremes


Admission requirements

This is a Master level course, basic knowledge of probability theory (IKR) and measure theory is required.


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.


You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

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.


Please register for the course in MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December.

Please note that it is compulsory to register your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Not being registered for an exam means your grade will not be processed.


Rajat Hazra (
Michel Mandjes (