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105.047
Non life insurance mathematics
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2007S, VO, 3.0h, 4.5EC
Properties
Semester hours: 3.0
Credits: 4.5
Type: VO Lecture
Aim of course
The collective risk model plays a central in non-life insurance mathematics. We present different ways to model the arrival process of claims and the claim sizes. We discuss tools for the exploratory statistical data analysis and we illustrate the theoretical methods using real data sets. The second part of the course introduces experience rating, Bayes estimation, and reserving for late claims.
Subject of course
(I) Collective Risk Models: Homogeneous and inhomogeneous Poisson processes, order statistics property, Poisson random measure, Cramér-Lundberg model, renewal process, mixed Poisson process, order of magnitude of the total claim amount, claim size distributions, heavy- and light-tailed distributions, exploratory statistical analysis with quantile-quantile plots and mean excess plots, regularly varying claim sizes and their aggregation, subexponential distributions, mixture distributions, space-time decomposition of a compound Poisson process, calculation of the distribution of the total claim amount using the extended Panjer recursion, approximation by the central limit theorem or Monte Carlo techniques, reinsurance treaties (II) Experience Rating: Heterogeneity model and Bayes estimation, linear Bayes estimator, credibility estimator, Bühlmann model, Bühlmann-Straub model (III) Reserving for Late Claims: Chain ladder method, grossing-up method, multiplicative model, multinomial model
Lecturers
Grandits, Peter
Institute
E105 Institute of Statistics and Mathematical Methods in Economics
Course dates
Day
Time
Date
Location
Description
Thu
09:00 - 11:00
01.03.2007 - 29.06.2007
Sem.R. DA grün 06A
GRANDITS
Mon
12:30 - 13:45
05.03.2007 - 29.06.2007
FH Hörsaal 2
SCHMOCK
Show single appointments
Non life insurance mathematics - Single appointments
F
P
1
2
N
E
Day
Date
Time
Location
Description
Thu
01.03.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
05.03.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
08.03.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
12.03.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
15.03.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
19.03.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
22.03.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
26.03.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
29.03.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
02.04.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
05.04.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
09.04.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
12.04.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
16.04.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
19.04.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
23.04.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
26.04.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
30.04.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
Thu
03.05.2007
09:00 - 11:00
Sem.R. DA grün 06A
GRANDITS
Mon
07.05.2007
12:30 - 13:45
FH Hörsaal 2
SCHMOCK
F
P
1
2
N
E
Examination modalities
Written and oral examination.
Exams
Day
Time
Date
Room
Mode of examination
Application time
Application mode
Exam
Tue
14:00 - 16:00
25.06.2024
FH Hörsaal 1 - MWB
written
01.04.2024 00:00 - 18.06.2024 23:59
TISS
Prüfung 2024S
Tue
12:00 - 14:00
24.09.2024
FH Hörsaal 1 - MWB
written
01.03.2024 00:00 - 17.09.2024 23:59
TISS
Prüfung 2024S (Nebentermin)
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Course registration
Not necessary
Curricula
Study Code
Obligation
Semester
Precon.
Info
No records found.
Literature
Lecture notes for this course are available. Im Sekretariat der
Forschungsgruppe FAM
erhältlich
Chapters 1 to 3 as well as 5 and 6 in the book by
Thomas Mikosch
, Non-Life Insurance Mathematics, An Introduction with Stochastic Processes, Springer Universitext, Springer-Verlag Berlin Heidelberg 2004, ISBN 3-540-40650-6.
Chapter 11 in the book by
Klaus D. Schmidt
, Versicherungsmathematik, Springer-Verlag Berlin Heidelberg 2002, ISBN 3-540-42731-7.
Accompanying courses
105.043 UE Non-life insurance mathematics
Language
German