NB! Lecture/forelesning

In our last lessons (8. Feb.-1. March) we studied the exact asymptotics of ruin probabilities in the case of small and large claim sizes, by using Smith´s key renewal theorem and the theory of regularly varying functions. See Chapter 1 in the book of Embrechts.

Further (2.-9. March) we discussed 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.

Next time (15./16. March) we want to address 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:

End of 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.