KFPOMI Actuarial Theory I

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Červinek (lecturer)
Guaranteed by
prof. Ing. Jiří Dvořák, DrSc.
Department of Finance – Faculty of Economics and Administration
Contact Person: Iva Havlíčková
Timetable
Sat 4. 10. 12:50–16:15 P312, Sun 23. 11. 8:30–11:50 P312, Sun 14. 12. 8:30–11:50 P312
Prerequisites
Actuarial mathematics builds on the knowledge of mathematics and statistics, financial mathematics, insurance and insurance economics.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
On the basis of the probability theory students will get acquainted with the design and use of mortality tables and their importance in life insurance. Using calculations based on the patterns derived from a single, ordinary and net premium of short-term insurance the students will be able to understand the issue of basic types of insurance. They will become also familiar with the general equation of equivalence and its use.

The main objectives of the course are the following:
Understanding the fundamentals of actuarial methods and procedures of calculating the basic characteristics of the classic types of insurance;
understanding of the principles of the calculations in the actuarial mathematics; the ability to solve independently problems even of non-standard insurance
Syllabus
  • Theme plan - Lectures
  • 1) Basic concepts, basic principles of insurance, insurance companies’ risk.
  • 2) Mortality tables, commutating numbers and their use.
  • 3) Single premium life insurance (in case of death, life age x+n and its combination, temporary insurance in case of death).
  • 4) Single mixed insurance, life insurance with guard period, normally paid premiums for life insurance. General equation of equivalence and its use for calculations.
  • 5) Premiums for life insurance paid m-times per year, risk of insurance companies in life insurance premiums.
  • 6) Gross premiums for life insurance and its calculation.
  • 7) Single premiums for pension insurance (life before-date immediate and after-date insurance, temporary insurance before-date and after-date).
  • 8) Single premiums for life insurance, retirement and deferred temporary.
  • 9) Current and short-term premiums for life insurance and deferred temporary retirement. Payable annually and m-times per year.
  • 10) Gross premiums for pension insurance.
  • 11) Net reserve for certain types of life and pension insurance. General formula for calculation of net reserves. Zillmer reserve.
  • 12) Actuarial calculations based on net and gross reserve (calculation of surrender, reduction of insured amount in unpaid premiums, reserve balance and profit sharing)
  • 13) insurance for two people - mortality tables for pair of people, probability of life for two people, probability of death of two people, commutating number, pair of life insurance, retirement insurance for two people (first death, second death, from first to second death).
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
  • 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
  • ČÁMSKÝ, František. Pojistná matematika v životním a neživotním pojištění (Insurence matematics of insurence life). 2004th ed. Brno: Vydavatelství MU, Brno-Kraví hora, 2005, 153 pp. ISBN 80-210-3385-1. 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
Assessment methods
Students are supposed to submit a seminar paper referred to as a POT. The deadline for its submission is the day before the last tutorial.
In the last tutorial the students will take an in-term test covering all the topics discussed in all previous tutorials.
If a student can not attend the in-term test or fails it, she/he is allowed to take a substitute in-term test, but no more than once.
There will be only one possibility to sit for the substitute in-term and the date on which it will be taken will be the same for all the students.
The test is written and oral.
The admission to the exam is subject to accepting the seminar paper by the tutor and passing the in-term test (i.e. at least 50% success rate).
The final grade is made up of:
Assessment of the in-term test (25%) + assessment of the written test (50%) + assessment of the oral exam (25%).
Grading scheme is the following:
A = 91 - 100%
B = 84 - 90%
C = 76 - 83%
D = 68 - 75%
E = 60 - 67%
F = less than 60%

If a student commits a prohibited act, such as using various forbidden tools (e.g. cheatsheets), cribbing, taking out any part of the test or any other form of cheating, the teacher is allowed to interrupt the test and to grade the student with F, FF or even FFF, according to the seriousness of the offence. The described procedure applies to all the activities that are included in the final evaluation of the course (semester paper). In case of a serious offense the tutor can iniciate an opening of disciplinary proceedings with the Disciplinary Committee.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Autumn 2006, Autumn 2007.
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