MPF_POMA Actuarial Theory

Faculty of Economics and Administration
Autumn 2010
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Červinek (lecturer)
Mgr. Petr Červinek (seminar tutor)
Guaranteed by
Mgr. Petr Červinek
Department of Finance – Faculty of Economics and Administration
Contact Person: Iva Havlíčková
Timetable
Mon 8:30–10:05 P403
  • Timetable of Seminar Groups:
MPF_POMA/01: Mon 12:50–14:30 VT203, P. Červinek
MPF_POMA/02: Mon 18:00–19:35 VT203, P. Červinek
MPF_POMA/03: Mon 16:20–17:55 VT203, P. Červinek
Prerequisites
! PFPOMI Actuarial Theory I
Actuarial mathematics builds on the knowledge of mathematics and statistics, financial mathematics, insurance.
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
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
  • 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, the 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, the 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 (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
  • 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
Teaching methods
lectures, during the seminars - solving of problems related to netto and brutto premium, reserving and policy changes
Assessment methods
Type of instruction: 2 / 2 (lecture / exercises)
Exam: Written
1.Control test I and test II, in the seminars students will write in weeks according to the timetable (if a student can not physically attend any (but no more than one) of the planned tests - excuse assess teacher - he may be allowed by the teacher to complete an alternative test of the entire subject matter in early examination period, the evaluation of alternative test will be consistent with the assessment of the tests)
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 at least 70% attendance at seminars; condition for the successful completion of each of the 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).
Each test consists of three problems of different difficulty.

The final mark is made up of:
Control test I assessment (25%) + evaluation Control Test II (25%) + Final test (50%)

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%

If the student uses during the tests illegal acts such as the use of illegal equipment, copying, obtaining the award of the tests and even anti-course tests, teachers interrupted the test and according to the gravity of the offense to grant class IS F, or FF, or and the FFF. In the case of a serious offense will be triggered Disciplinary Board disciplinary proceedings.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Nezapisují si studenti, kteří absolvovali předmět PFPOMI.
Credit evaluation note: k=1.
The course is also listed under the following terms Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
  • Enrolment Statistics (Autumn 2010, recent)
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