M5KPM Chapters from actuarial mathematics

Faculty of Science
Autumn 2025
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Mgr. Silvie Zlatošová, Ph.D. (lecturer)
Guaranteed by
Mgr. Silvie Zlatošová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 11:00–12:50 M6,01011
  • Timetable of Seminar Groups:
M5KPM/01: Wed 13:00–13:50 M6,01011, S. Zlatošová
Prerequisites
M6110 Mathematics of Insurance
M6110
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to teach students some important techniques from insurance mathematics. At the end of this course, students will be able to understand the collective and individual risk models and apply them. Based on the acquired knowledge student should also be able to determine tariff rates in different periods and credibility and Bayesian premiums.
Learning outcomes
At the end of this course, students will be able to understand the collective and individual risk models and apply them. Based on the acquired knowledge student should also be able to determine tariff rates in different periods and credibility and Bayesian premiums.
Syllabus
  • Thematic Plan
  • -Building the conceptual and computational framework for the introduction of the collective and individual risk model
  • 1. Distribution of the number of insurance claims I
  • 2. Distribution of the number of insurance claims II
  • 3. Distribution of the number of insurance claims III
  • 4. Distribution of the size of insurance claims I
  • 5. Distribution of the size of insurance claims II
  • 6. Distribution of the size of insurance claims III
  • 7. Models of the aggregate insurance claim I
  • 8. Models of the aggregate insurance claim II
  • 9. Midterm test
  • -Credibility Theory
  • 10. Basic concepts of credibility theory
  • (heterogeneity, homogeneous risk, full and partial credibility)
  • 11. Limited fluctuation theory
  • (problem formulation, approaches to premium calculation, issues of limited fluctuation theory, applications with examples)
  • 12. Optimal credibility theory
  • (introduction of the risk parameter, Bayesian methodology, individual premium, collective premium)
  • 13. Optimal credibility theory
  • (Bayesian premium, credibility premium, Bühlmann model, applications with examples)
  • 14. Retake test + substitute test
Literature
    required literature
  • TSE, Yiu Kuen. Nonlife actuarial models : theory, methods and evaluation. Second edition. Cambridge: Cambridge University Press, 2023, xiv, 535. ISBN 9781009315074. info
  • KLUGMAN, Stuart A.; Harry H. PANJER and Gordon E. WILLMOT. Loss models : from data to decisions. 4th ed. Hoboken, N.J.: John Wiley & Sons, 2012, xiv,511 s. ISBN 9781118315323. info
  • BOWERS, Newton L. Actuarial mathematics. 2nd ed. Schaumburg, Ill.: Society of Actuaries, 1997, xxvi, 753. ISBN 0938959468. info
    recommended literature
  • MANDL, Petr and Lucie MAZUROVÁ. Matematické základy neživotního pojištění. Vyd. 1. Praha: Matfyzpress, 1999, 113 s. ;. ISBN 80-85863-42-1. info
Teaching methods
Lectures and discussion. Practical examples in tutorials. Homeworks.
Assessment methods
Course Completion Requirements:
During the semester, 1 midterm test is written. It is possible to earn 15 points from it.
The exact date of the test will be announced by the instructor at least 14 days in advance.
To be admitted to the final exam, it is necessary to obtain at least 8 points from this test.


The exam is written.
To successfully complete the course, it is necessary to obtain at least 18 points in total.

The regular exam will take place at the beginning of the examination period. The exam will cover the material not included in the midterm test during the semester. The written exam will be graded with 15 points. The total score will be calculated as the sum of the points from the midterm test during the semester and the written exam in the regular term.

In case of failure, the student is entitled to a retake. This retake will cover the material from the entire semester, and the written exam will be graded with 30 points. The total score will then be based solely on the result of the retake exam.

A student who does not obtain at least 18 points will receive the grade F.

A necessary condition for successful completion of the course is having no more than 3 unexcused absences from tutorials.


The conditions may be adjusted depending on the development of the epidemiological situation and the applicable restrictions.
Language of instruction
Czech
Further Comments
Study Materials
The course is also listed under the following terms Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
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