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Life Insurance Mathematics
Prof. Dr. Frederik Herzberg
Synopsis
This course provides an introduction to life insurance mathematics broadly conceived, covering insurances against all life-contingent risks, with a particular emphasis on the regulatory framework in Germany. Topics include:
- Multiple-decrement models and actuarial calculation bases
- Expected present values of payment streams (for premiums and benefits)
- Equivalence principle and actuarial reserves
- Applications of the above: e.g., whole life insurance, annuities, pensions, private health insurance (according to German law)
- Survival functions, hazard rates and the construction of life tables
Depending on the participants' level of proficiency in German, the lecture course may be taught partly in German.
Lectures
- Thursdays, 12:15pm-13:45pm, seminar room 6 (building E2 4, room 2.17)
- Start date: 15 October
Recommended Prerequisites
Stochastik I (i.e., introductory measure-theoretic probability theory)
In addition, some familiarity with Mathematical Statistics will be helpful for the chapter on survival models, but is not an absolute prerequisite.
Tutorials
TBA
Exam
After the end of the semester, there will be an oral exam. For exam admission, regular active participation in the tutorials is required.
References
There is no unique textbook that would cover all the material of this lecture course. Nevertheless, parts of the following textbooks can be useful for different parts of the lecture course:
- Dickson, Hardy & Waters: Acturial mathematics for life-contingent risks. Cambridge University Press
- Gerber: Life insurance mathematics. Springer
- Milbrodt & Helbig: Mathematische Methoden der Personenversicherung. Walter de Gruyter
- O'Quigley: Survival analysis. Proportional and non-proportional hazards regression. Springer
A detailed summary of the contents of the lecture course is contained in the following document (in German) by the German Association of Actuaries (DAV):
- Deutsche Aktuarvereinigung: Leitfaden Versicherungsmathematik (Kapitel 3-6)
- Deutsche Aktuarvereinigung: Leitfaden Angewandte Stochastik (Kapitel 2)
→ Course reference shelf, kindly provided by the Campus-Bibliothek für Informatik und Mathematik