Risk Theory 2 - NMFP531
Title: Teorie rizika 2
Form of teaching: lecture+practicals
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2026
Duration in semesters: 1
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Maximum number of enrolled students: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information: https://dl1.cuni.cz/course/view.php?id=15604
Repeated enrollment: 2 / 2 / 2 / 2
Guarantor: RNDr. Lucie Mazurová, Ph.D.
Teacher(s): RNDr. Daniela Flimmel, Ph.D.
RNDr. Lucie Mazurová, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Povinně volitelné
Classification: Mathematics > Financial and Insurance Math.
Is incompatible with: NMFM503
Is pre-requisite for: NMFP558
Opinion survey results   WS schedule   Noticeboard   
Annotation -
Multiple state models in insurance. Bonus-malus systems in automobile insurance. Modeling bonus systems using discrete-time Markov chains. Multiple state models in disability insurance. Estimation of transition intensities. Construction of an increment-decrement table. Actuarial calculations.
Last update: Branda Martin, doc. RNDr., Ph.D. (13.12.2020)
Aim of the course -

Introduction to multiple state models and bonus-malus systems.

Last update: Zichová Jitka, RNDr., Dr. (06.05.2026)
Course completion requirements -

Requirements to successfully pass the practicals: Elaboration of two extensive homeworks assigned during the semester. If the solution is unsatisfactory, homework assignments may be resubmitted.

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

Last update: Mazurová Lucie, RNDr., Ph.D. (28.08.2026)
Literature -

M. Denuit, X. Maréchal, S. Pitrebois, J.-F. Walhin: Actuarial Modelling of Claim Counts. John Wiley & Sons, 2007.

S. Haberman, E. Pitacco: Actuarial Models for Disability Insurance. Chapman & Hall / CRC, 1999.

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

Lecture + exercises.

Last update: Zichová Jitka, RNDr., Dr. (09.05.2023)
Course assessment methods and requirements for successful completion, grading scheme -

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

Last update: Mazurová Lucie, RNDr., Ph.D. (03.10.2024)
Syllabus -

1. Bonus-malus system: transition rules, modeling by means of a discrete-time Markov chain, stationary distribution, optimal relativities, interaction with a priori ratemaking, measures of efficiency.

2. Multiple state models in disability insurance: modeling by means of continuous-time Markov chains, transition intensities and their estimation, transition probabilities, construction of an increment-decrement table, calculation of premius and reserves.

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