Lecture/forelesning

In our last lessons (21. Feb.-15. March) we studied the exact asymptotics of ruin probabilities in the case of large claim sizes, by using e.g. mathematical tools from the theory of regularly varying functions. See Chapter 1 in the book of Embrechts.

Then, we continued with the discussion one of the main results of extreme value theory, that is the theorem of Fisher-Tippett-Gnedenko, which can be regarded as a central limit theorem for maximal claims (Ch. 3 in Embrechts). The latter result is also important for the practical study of large claims, which may cause the spontaneous ruin of an insurance company.

In addition, we have addressed the problem of the characterization of the maximum domain of attraction of extreme value distributions.

Our study plan for the next weeks is the following:

March: Discussion of convergence rates with respect to the Fisher-Tippett-Gnedenko theorem and statistical methods for extreme value distributions (Ch. 3 and 6 in Embrechts). 

April/May: Study of extremal events from the viewpoint of point processes (Ch. 5 in Embrechts) and large deviation techniques.