Mathematics of Non-Life Insurance (FS 2017)

 

Lecturer and Assistant

Prof. R. Gatto, gatto@stat.unibe.ch, 031 631 8807, office 010, Alpeneggstrasse 22, Sprechstunde nach Vereinbarung

F. Wespi, florian.wespi@stat.unbe.ch, 031 631 8813, office 004, Alpeneggstrasse 22, Sprechstunde nach Vereinbarung

 

Time and place

Thursday, 14-17, B78

Friday,     12-13, B78 

 

General information

- Lecture intended for students in the following programs:

  B.Sc. in Mathematics (Haupt- oder Spezialisierungsmodul)

  M.Sc. in Mathematics (Gefäss Stochastik)

  M.Sc. in Statistics (Gefäss Finanz- und Versicherungsmathematik)

- Prerequisites: undergraduate probability theory and statistics

- General participation to lecture and exercises required for exam 

 

Syllabus

1. Individual risks and distributions

Individual risks and distributions

Hazard rate and mean excess loss function

Pareto-type and subexponential distributions

Risk measures

Copulas

 

2. Risk process and ruin theory

Birth processes and compound processes

Risk process

Integro-differential equation

Aggregate loss process and maximal aggregate loss

Exact inversion formula for the probability of ruin

Heavy- and light-traffic approximations

Renewal theory

 

Reference

Gatto, R. (2014), Stochastische Modelle der Aktuariellen Risikotheorie - Eine Mathematische Einfuehrung, Springer.

 

Assignments

24.02 Lecture (no assignment)

03.03 Discussion of Assignment 1: 2.6.1, 2.6.2, 2.6.3, 2.6.5, 2.6.6, 2.6.7

10.03 Discussion of Assignment 2: 2.6.8, 2.6.9, 2.6.11, 2.6.13

17.03 Discussion of Assignment 3: 2.6.15, 2.6.16

24.03 Lecture (no assignment)

31.03 Lecture (no assignment)

07.04 Discussion of Assignment 4: assignment4.pdf (PDF, 97KB)assignment4_sol.pdf (PDF, 124KB)

13.04 Online solution of Assignment 5: 3.6.1, 3.6.2, 3.6.3, 3.6.4

28.04 Discussion of Assignment 6: 3.6.5, 3.6.6, 3.6.12, 3.6.14

05.05 Discussion of Assignment 7: 3.6.19, 4.9.5, 4.9.11

12.05 Discussion of Assignment 8: assignment8.pdf (PDF, 103KB)assignment8_sol.pdf (PDF, 103KB)

19.05 Discussion of Assignment 9: 4.9.3, 4.9.4

26.05 Discussion of Assignment 10: 4.9.6, 4.9.8, 4.9.10

02.06 Online solution of Assignment 11: 4.9.7, 4.9.9 No discussion but question/answer session instead

 

Exam

Oral examination

First session: June 2017

Friday June 16, Room B78 (ExWi)

09:30 - 10:00 B. Balmer

10:00 - 10:30 B. Polanco

10:30 - 11:00 F. Perler

Break

11:30 - 12:00 J. Loeffler 

12:00 - 12:30 A. Zarotiadou

12:30 - 13:00 A. Carrera

Break

14:30 - 15:00 M. Bichsel

15:00 - 15:30 K. Levitin

Thursday June 22, Room 228 (ExWi)

09:30 - 10:00  T. Haering

10:00 - 10:30 M. Pfeuti  

10:30 - 11:00 Y. Tercier

Break

11:30 - 12:00 X. Garcia

12:00 -12:30 L. Pozzi