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Course, academic year 2022/2023
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Mathematics of Non-Life Insurance 1 - NMFP409
Title: Matematika neživotního pojištění 1
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022 to 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter 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
Additional information:
Guarantor: RNDr. Lucie Mazurová, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
Classification: Mathematics > Financial and Insurance Math.
Incompatibility : NMFM401
Interchangeability : NMFM401
Is incompatible with: NMFM401
Is pre-requisite for: NMFP501, NMFP434, NMFP532
Is interchangeable with: NMFM401
Annotation -
Last update: doc. RNDr. Martin Branda, Ph.D. (13.12.2020)
Probabilistic modeling of claim sizes, claim counts and aggregate losses. Application of the collective model in ruin theory and in reinsurance. Introduction to classification ratemaking. Basic methods of claims reserving.
Aim of the course -
Last update: RNDr. Jitka Zichová, Dr. (02.06.2022)

The aim of the subject is to describe probabilistic models used in non-life insurance, fundamentals of the collective risk model including elementary ruin theory , to make a survey of technical reserves and selected methods for computing outstanding claims reserves.

Course completion requirements -
Last update: Mgr. Ing. Pavel Kříž, Ph.D. (13.10.2022)

Conditions for the exercise class credit: solved homeworks, written exam (at least 50% of points), oral presentation on a given topic.

The nature of these requirements precludes possibility of additional attempts to obtain the exercise class credit.

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

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

S.A. Klugman, H.H. Panjer, G.E. Willmot: Loss Models: From Data to Decisions. John Wiley & Sons, 1998.

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

P. Mandl, L. Mazurová: Matematické základy neživotního pojištění. MatfyzPress, 1999.

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

Lecture + exercises.

Requirements to the exam -
Last update: RNDr. Lucie Mazurová, Ph.D. (12.10.2022)

Oral exam with written preparation. Requirements for the exam consist of the entire extent of the lecture.

Syllabus -
Last update: RNDr. Lucie Mazurová, Ph.D. (13.12.2020)

1. Distributions of claim sizes derived by a power transform, generalized and generalized inverse distributional families. Tail behavior, subexponential distributions.

2. (a,b,0) and (a,b,1) classes of counting distributions.

3. Panjer recursive formula for compound distributions. Methods of discretization of a continuous claim size distribution. Calculation of a compound distribution by means of FFT. Approximations of the aggregate loss distribution.

4. Discrete-time ruin theory model.

5. Pricing of XL-reinsurance with reinstatements.

6. Simple methods of classification ratemaking. Loglinear model.

7. Mack's model and chain-ladder method. Bornhuetter-Ferguson method. Poisson model for incremental development triangles.

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