PřF:M6110 Mathematics of Insurance - Course Information
M6110 Mathematics of Insurance
Faculty of ScienceSpring 2025
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 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
- Mon 17. 2. to Sat 24. 5. Tue 12:00–13:50 M6,01011
- Timetable of Seminar Groups:
- Prerequisites
- M2120 Mathematics of Finance I
Actuarial mathematics builds on the knowledge of mathematics and statistics, financial mathematics, insurance. - Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives
- After passing the course is student able to: make clear the fundamentals of actuarial mathematics, make clear the methods and the procedures of calculating the basic characteristics of the classic types of insurance, apply the principles of the calculations in the actuarial mathematics, solve independently problems even of non-standard insurance.
- Learning outcomes
- After passing the course is student able to: make clear the fundamentals of actuarial mathematics, make clear the methods and the procedures of calculating the basic characteristics of the classic types of insurance, apply the principles of the calculations in the actuarial mathematics, solve independently problems even of non-standard insurance.
- Syllabus
- Thematic Plan - Lectures
- 1. Basic concepts, fundamental principles of insurance, insurance company risks.
- (insurance risk, insurance relationship, insurable risks, life insurance, non-life insurance, principles – solidarity, conditional return, non-equivalence, risks arising from business and insurance activities of an insurance company, actuarial risk of an insurance company)
- Life Insurance
- 2. Survival models
- (future lifetime, mortality intensity, laws of mortality, actuarial notation)
- 3. Mortality tables and selection
- (mortality tables, commutation numbers, assumption of fractional ages, selection process, selective survival model)
- 4. Insurance benefits and their value for death and survival insurance.
- (Death insurance - continuous, annual, and 1/m annual payment cases, recursive formula, whole life and term insurance. Survival insurance.)
- 5. Insurance benefits and their value for mixed insurance, deferred forms of insurance, annuity (pension) insurance.
- (mixed insurance, pension insurance (due, immediate, whole life, temporary, deferred, increasing and decreasing sum assured, guaranteed pensions))
- 6. Calculation of single premium, calculation of regular net premium, general equivalence equation.
- (derivation of formulas + examples)
- 7. Gross premium in life insurance and its calculation.
- (distribution of insurance company costs, initial costs, regular administrative costs, collection costs, gross premium paid as a single or regular payment)
- 8. Technical reserves in personal insurance.
- (classification of technical reserves, life insurance premium reserve, calculation of net reserve, saving and risk components of premium)
- 9. Zillmer reserve, actuarial calculations based on net and gross reserves.
- (calculation of Zillmer reserve, surrender value, calculation of reduced sum assured, change of insurance type, dynamization)
- Non-Life Insurance
- 10. Tariff groups and basic indicators, gross premium.
- (pricing examples, statistical insurance indicators – average insurance benefit, claim frequency, claim severity, general net premium formula, premium calculation - pure interest insurance, full-value insurance, first-risk insurance, deductibles - proportional, excess, integral)
- 11. Technical reserves, calculation of claims reserve.
- (gross premium – safety loading, classification of technical reserves, calculation of claims reserves using triangle methods - chain ladder method, separation method)
- 12. Bonus-malus system, Markov analysis.
- (basic concepts, Markov analysis, transition probability matrix between groups, system state after t years, stationary vector – steady-state of the system, bonus hunger)
- 13. Basics of individual risk modeling.
- (introduction to risk theory, models of claim count and claim size, basic probability distributions for claim count and claim size, insurance models over time)
- Thematic Plan – Seminars
- Students will independently solve problems applying the theoretical foundations of actuarial mathematics from the lecture topics and their own studies. At the end of the semester, project presentations will take place during the exercises.
- Literature
- recommended literature
- PROMISLOW, S. David. Fundamentals of actuarial mathematics. Chichester: John Wiley & Sons, 2006, xix, 372. ISBN 0470016892. info
- GERBER, Hans U. Life insurance mathematics. Edited by Samuel H. Cox. 3rd ed. Zurich: Springer, 1997, xvii, 217. ISBN 354062242X. info
- MILBRODT, Hartmut and Manfred HELBIG. Mathematische Methoden der Personenversicherung. Berlin: Walter de Gruyter, 1999, xi, 654. ISBN 3110142260. info
- BOOTH, P. Modern actuarial theory and practice. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2005, xxxiii, 79. ISBN 1584883685. info
- MØLLER, Thomas and Mogens STEFFENSEN. Market-valuation methods in life and pension insurance. 1st ed. Cambridge: Cambridge University Press, 2007, xiv, 279. ISBN 9780521868778. info
- not specified
- DICKSON, D. C. M., Mary HARDY and H. R. WATERS. Actuarial mathematics for life contingent risks. 2nd ed. Cambridge: Cambridge University Press, 2013, xxi, 597. ISBN 9781107044074. info
- CIPRA, Tomáš. Pojistná matematika : teorie a praxe. 2., aktualiz. vyd. Praha: Ekopress, 2006, 411 s. ISBN 8086929116. info
- Teaching methods
- lectures, during the seminars - solving of problems related to netto and brutto premium, reserving and policy changes. In seminars, students independently solve assigned tasks. Some tasks will be solved using the R language.
- Assessment methods
- Requirements for Course Completion:
- During the semester, students will complete a project using the R programming language. The project will address a selected problem and apply the techniques covered in the course.
- Students will defend this project during the exercise session at the end of the semester.
- Students will also evaluate the assigned projects of their randomly selected peers and provide feedback.
- For these activities, students can earn up to 20 points. To be allowed to take the final exam, at least 12 points must be earned.
- The final exam is written, and a maximum of 30 points can be awarded. The student will solve problems or exercises covered in the lectures and exercises, possibly including theoretical questions. To pass the exam, the student must score at least 18 points.
- The points from the semester and the written exam are summed, and the student receives a grade according to the following scale:
A: [46; 50]
B: [42; 46)
C: [38; 42)
D: [34; 38)
E: [30; 34)
F: [0; 30).
Any form of cheating, recording or removing tests, using unauthorized aids as well as communication tools, or other disruptions to the objectivity of the exam (or credit) will be considered a failure to meet the course requirements and a serious violation of academic regulations. As a result, the instructor will assign a grade of "F" in the university system, and the Dean will initiate disciplinary proceedings, which could result in expulsion from the university. - Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/spring2025/M6110