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105.047
Non life insurance mathematics
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.
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2010S, 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
12:00 - 13:15
04.03.2010 - 30.06.2010
FH Hörsaal 2
SCHMOCK
Mon
12:00 - 13:15
08.03.2010 - 30.06.2010
FH Hörsaal 2
GRANDITS
Show single appointments
Non life insurance mathematics - Single appointments
F
P
1
2
N
E
Day
Date
Time
Location
Description
Thu
04.03.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
08.03.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
11.03.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
15.03.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
18.03.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
22.03.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
25.03.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
29.03.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
01.04.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
05.04.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
08.04.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
12.04.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
15.04.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
19.04.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
22.04.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
26.04.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
29.04.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
03.05.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
Thu
06.05.2010
12:00 - 13:15
FH Hörsaal 2
SCHMOCK
Mon
10.05.2010
12:00 - 13:15
FH Hörsaal 2
GRANDITS
F
P
1
2
N
E
Examination modalities
oral and written exam The written exam can be taken at one of three dates during the semester. Dates and details can be found here:
http://www.fam.tuwien.ac.at/lehre/pr/index.php
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)
Register for an exam
Course registration
Not necessary
Curricula
Study Code
Obligation
Semester
Precon.
Info
033 205 Financial and Actuarial Mathematics
Mandatory
6. Semester
033 215 Actuarial Mathematics
Mandatory
4. Semester
066 400 Mathematics
Mandatory elective
066 401 Statistics
Mandatory elective
066 402 Mathematics in Science and Technology
Mandatory elective
066 403 Mathematics in Economics
Mandatory elective
066 404 Mathematics in Computer Science
Mandatory elective
066 405 Financial and Actuarial Mathematics
Mandatory elective
860 Technical Mathematics
Mandatory elective
864 Mathematics for Natural Sciences
Mandatory elective
866 Economic Mathematics
Mandatory elective
867 Statistics
Mandatory elective
869 Mathematics in Computer Science
Mandatory elective
873 Finance and Actuarial Mathematics
Mandatory
873 Finance and Actuarial Mathematics
Mandatory
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