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Course, academic year 2022/2023
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Mathematics of Non-Life Insurance 2 - NMFP434
Title: Matematika neživotního pojištění 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022 to 2022
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Lucie Mazurová, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Povinně volitelné
Classification: Mathematics > Financial and Insurance Math.
Incompatibility : NMFM402
Pre-requisite : NMFP409
Interchangeability : NMFM402
Is incompatible with: NMFM402
Is interchangeable with: NMFM402
Annotation -
Last update: doc. RNDr. Martin Branda, Ph.D. (13.12.2020)
Point processes and their application in modeling the arrival of insurance claims in time. Bayesian credibility theory. GLM in reserving. Mean square error of a loss reserve estimate.
Aim of the course -
Last update: RNDr. Jitka Zichová, Dr. (02.06.2022)

The aim of the subject is to make the students aquainted with selected mathematical methods used in non-life insurance rate-making.

Course completion requirements -
Last update: RNDr. Lucie Mazurová, Ph.D. (15.05.2023)

Conditions for the exercise class credit: solved homework.

The exercise class credit is necessary for the participation in the exam.

Literature -
Last update: doc. RNDr. Martin Branda, Ph.D. (13.12.2020)

H. Panjer, G.E. Willmot: Insurance risk models. Society of Actuaries, 1992.

E. Ohlsson, B. Johansson: Non-life Insurance Pricing with Generalized Linear Models. Springer, 2010.

H. Bühlmann, A. Gisler: A Course in Credibility Theory and its Applications. Springer, 2005.

M.V. Wüthrich, M. Merz: Stochastic Claims Reserving Methods in Insurance. Wiley, 2008.

Teaching methods -
Last update: RNDr. Jitka Zichová, Dr. (02.06.2022)

Lecture + exercises.

Syllabus -
Last update: RNDr. Lucie Mazurová, Ph.D. (12.12.2020)

1. Poisson process, processes with an intensity depending on time and state. Renewal processes.

2. Application of GLM in a multiplicative tariff structure. Models of claim frequency and claim severity.

3. Application of GLM in the analysis of development triangles. Mean square error of the IBNR reserve prediction and its estimate.

4. Bühlmann and Bühlmann - Straub models of credibility theory. Application in a multiplicative tariff structure and in reserving.

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