# 105.047 Non life insurance mathematics This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2024S 2023S 2022S 2021S 2020S 2019S 2018S 2017S 2016S 2015S 2014S 2013S 2012S 2011S 2010S 2009S 2008S 2007S 2006S 2005S 2004S

2009S, 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

## Course dates

DayTimeDateLocationDescription
Mon12:00 - 13:1502.03.2009 - 30.06.2009FH Hörsaal 2 SCHMOCK
Thu09:00 - 11:0005.03.2009 - 30.06.2009Sem.R. DA grün 06A SCHMOCK
Non life insurance mathematics - Single appointments
DayDateTimeLocationDescription
Mon02.03.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu05.03.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon09.03.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu12.03.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon16.03.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu19.03.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon23.03.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu26.03.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon30.03.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu02.04.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon06.04.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu09.04.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon13.04.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu16.04.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon20.04.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu23.04.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon27.04.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu30.04.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK
Mon04.05.200912:00 - 13:15FH Hörsaal 2 SCHMOCK
Thu07.05.200909:00 - 11:00Sem.R. DA grün 06A SCHMOCK

## Examination modalities

Written and oral examination. 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

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Tue12:00 - 14:0024.09.2024FH Hörsaal 1 - MWB written01.03.2024 00:00 - 17.09.2024 23:59TISSPrüfung 2024S (Nebentermin)
Tue15:00 - 17:0004.03.2025FH Hörsaal 1 - MWB written01.01.2025 00:00 - 25.02.2025 23:59TISSPrüfung 2024S (letzter Termin)
Mon14:00 - 16:0030.06.2025FH Hörsaal 1 - MWB written01.03.2025 00:00 - 23.06.2025 23:59TISSPrüfung 2025S
Tue13:00 - 15:0023.09.2025FH Hörsaal 1 - MWB written01.07.2025 00:00 - 09.09.2025 23:59TISSPrüfung 2025S (Nebentermin)

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
033 205 Financial and Actuarial Mathematics Mandatory6. Semester
033 215 Actuarial Mathematics Mandatory4. 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.

German