PFPOMI Actuarial Theory I

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Červinek (lecturer)
Mgr. Petr Červinek (seminar tutor)
Guaranteed by
prof. Ing. Viktória Čejková, Ph.D.
Department of Finance – Faculty of Economics and Administration
Contact Person: Iva Havlíčková
Timetable
Mon 18:00–19:35 P312
  • Timetable of Seminar Groups:
PFPOMI/1: Mon 12:50–14:30 VT203, P. Červinek
PFPOMI/2: Mon 14:35–16:15 VT105, P. Červinek
PFPOMI/3: Mon 16:20–17:55 VT203, P. Červinek
Prerequisites
PFPOJI Insurance Industry && PMSTAI Statistics I
Actuarial mathematics builds on the knowledge of mathematics and statistics, financial mathematics, insurance and insurance economics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 80 student(s).
Current registration and enrolment status: enrolled: 0/80, only registered: 0/80, only registered with preference (fields directly associated with the programme): 0/80
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, the 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).
  • Theme plan - seminars
  • 1) Introductory seminar (organization of seminars, assessment and requirements for completion of course, use of mortality tables and commutation of numbers, likelihood of death or life; practical calculations)
  • 2) Calculation of single premium life insurance (insurance in event of death, life insurance age x + n; temporary insurance in event of death)
  • 3) Calculation of single premium life insurance (joint insurance, life insurance with guard period, temporary insurance in event of death)
  • 4) Calculation of insurance premiums for life insurance using general equivalency formula (insurance in event of death, temporary insurance in event of death, life insurance age x + n; temporary insurance in event of death; mixed insurance, life insurance with guard period)
  • 5) Calculation of insurance premiums for life insurance paid normally, and m-times per year, gross premiums for life insurance (normal premiums for life insurance, premiums paid m-times per year; risk insurance company in premiums for life insurance, gross premiums for life insurance)
  • 6) Calculation of one-off premium for pension insurance (life short-term insurance immediate and after-date income; temporary before-date and after-date income)
  • 7) In-term test I
  • 8) Calculation of one-off premium for pension insurance (deferred life annuity, temporary pension)
  • 9) Calculation of current and short-term insurance, gross premiums (life and temporary deferred pension paid annually, and m-times per year, gross premiums for pension insurance)
  • 10) Gross premiums for pension insurance (life before-date immediate and after-date income; temporary before-date and after-date pension, deferred life and temporary pension paid annually, gross premiums for pension insurance)
  • 11) Net margin (calculation of net reserves for certain types of life insurance, calculation of net reserves for certain types of pension contributions)
  • 12) Actuarial calculations based on net and gross reserve reserve (value, reduction of insured amount for non-payment of premiums; reserve balance, share of profits)
  • 13) In-term test II (specifications and development of Surveillance Test II; questions, arrangements for oral exam)
  • Students will be independently solving assignments and while doing so they are supposed to apply the theory of actuarial mathematics of individual lectures and self-study.
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
The course has a form of lectures and seminars (2 / 2).
Exam: Written and oral
1. Students will take the in-term test 1 and 2 in weeks according to the timetable (if a student can not physically attend either (but no more than one) of the planned tests - an excuse will be assessed by the teacher - he/she is allowed to sit for a substitute test of the entire course matter at the beginning of the examination period. The assessment of the substitute test will be consistent with the assessment of the other tests.
2. The final assessment of work in the seminars:
The admission to the exam is subject to passing the in-term tests and minimum 70% attendance in the seminars. Minimum success rate to pass the in-term tests is 60 %.
3. The exam and final assessment:
The exam has two parts - a written one consisting of a in-term test I and II and oral one.

The final grade is made up of:
The assessment of the in-term test I (25%) + the assessment of the in-term test II (25%) + oral exam (50%).

The 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 (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Předpokladem je i absolvování předmětu Finanční matematika nebo Finanční matematika pro FP.
The course is also listed under the following terms Autumn 2007.
  • Enrolment Statistics (recent)
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