M6110 Mathematics of Insurance

Faculty of Science
Spring 2021
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Mgr. Silvie Zlatošová, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Tue 18:00–19:50 online_M3
  • Timetable of Seminar Groups:
M6110/01: Mon 1. 3. to Fri 14. 5. Tue 17:00–17:50 online_M3, S. Zlatošová
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
  • Theme plan - Lectures
  • Life Insurance
  • 1) Basic concepts, basic principles of insurance, insurance companies’ risk.
  • 2) Mortality tables, commutating numbers and their use.
  • 3)Calculation of the single premium in case of deat and life age x+n.
  • 4)Calculation of the single mixed insurance, pension insurance.
  • 5)Insurance with fixed time payroll, calculation of the normally paid premiums, general equation of equivalence.
  • 6) Gross premiums for life insurance and its calculation.
  • 7) Reserve for certain types of life and pension insurance.
  • 8) Zillmer reserve, actuarial calculations based on the net and gross reserve.
  • Non-life Insurance
  • 9)Tariff groups and basic indicators in non-life insurance, gross premiums.
  • 10)Insurance reserves, calculation of the outstanding claims reserves.
  • 11)Bonus-malus systems, Markov analysis.
  • 12)Mathematical modeling (introduction to the theory of risk, models the number of claims).
  • 13) Mathematical modeling (models for claim amount, insurance models in time).
  • Theme plan - seminars
  • 1) Introductory seminar (organization of seminars, assessment and requirements for completion of course, use of mortality tables)
  • 2)Use of mortality tables and commutation of numbers, the likelihood of death or life; practical calculations)
  • 3)Calculation of the single premium in case of deat and life age x+n.
  • 4)Calculation of the single mixed insurance, pension insurance.
  • 5)Insurance with fixed time payroll, calculation of the normally paid premiums, general equation of equivalence.
  • 6)Calculation of the gross premiums for life insurance.
  • 7) In-term test I
  • 8)Calculation of the reserve for certain types of life and pension insurance.
  • 9) Zillmer reserve, actuarial calculations based on the net and gross reserve.
  • 10)Calculation of the outstanding claims reserves in non-life insurance.
  • 11)Bonus-malus systems, Markov analysis.
  • 12)Mathematical modeling
  • 13) In-term test II (specification and development of Surveillance Test II; questions, arrangements for oral exam)
  • Students will be independently solving assigments and while doing so they are supposed to apply the theory of actuarial mathematics of individual lectures and self-study.
Literature
    required literature
  • ČERVINEK, Petr. Pojistná matematika I (Actuarial Mathematics I). 1st ed. Brno: ESF MU, 2008, 73 pp. ISBN 978-80-210-4532-3. info
  • CIPRA, Tomáš. Pojistná matematika : teorie a praxe. Vyd. 1. Praha: Ekopress, 1999, 398 s. ISBN 8086119173. info
    recommended literature
  • ČÁMSKÝ, František. Pojistná matematika v životním a neživotním pojištění. 1. vyd. Brno: Masarykova univerzita, 2004, 115 s. ISBN 8021033851. info
  • 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
Teaching methods
lectures, during the seminars - solving of problems related to netto and brutto premium, reserving and policy changes. Homeworks.
Assessment methods
Type of instruction: 2 / 1 (lecture / exercises)
Exam: Written
1.Control test I and test II, in the seminars students will write in weeks according to the timetable.
2.Closing evaluation of the results of the work of the seminar (a condition of participation in the test is successful completion of the planned tests, and no more than 3 absences at seminars; condition for the successful completion of control tests is a formal evaluation of 60% or more)
3. The test results and evaluation (exam has two parts - through part, which consists of a Control test I and II Control test, and final part, which consists of a Final test).

The final mark is made up of:
Control test I assessment (10%) + evaluation Control Test II (10%) + Final test (80%)

To evaluate the performance of students in the test the following scale:
A = 92 - 100%
B = 84 - 91%
C = 76 - 83%
D = 68 - 75%
E = 60 - 67%
F = less than 60%

Any copying, recording or obtaining tests, use of unauthorized tools as well as other means of communication or objectivity distortion test (credit) will be considered as failure to comply with the course completion and a gross violation of regulations. Consequently, teacher close examination (credit) in the evaluation of IS grade "F" and the Dean initiates disciplinary proceedings which may result in up to exclusion from the study.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2021, recent)
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