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Course, academic year 2023/2024
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Life Insurance 2 - NMFM406
Title: Životní pojištění 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Tomáš Cipra, DrSc.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
Classification: Mathematics > Financial and Insurance Math.
Incompatibility : NMFP432
Pre-requisite : NMFM405
Interchangeability : NMFP432
Is co-requisite for: NMFM416
Is incompatible with: NMFP432
Is pre-requisite for: NMFM502, NMFM501
Is interchangeable with: NFAP048
In complex interchangeability with: NMFP432
Annotation -
Multiple decrements model. Multiple life insurance. Calculation of premiums and reserves including expense loadings. Pension funds.
Last update: T_KPMS (13.05.2013)
Aim of the course -

Students master life insurance mathematics on the level necessary to obtain the certificate of responsible actuary.

Last update: T_KPMS (13.05.2013)
Course completion requirements -

1) Active participation in 70% of total number of exercises.

2) Accomplishing 3 homeworks in given terms. If an error is found, the student must correct it and send it again.

3) Successfull passing the credit test in the end of semester: the student must achieve at least 7 points from 10. The test can be repeated at most once in the given term.

Remarks. The credit for the excersices is not condition for passing exam.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (02.02.2018)
Literature -

Dickson,D.C.M.,Hardy,M.R., Waters, H.R.: Actuarial Mathematics for Life Contingent Risks. Cambridge University Press, Cambridge 2012.

Cipra, T.: Financial and Insurance Formulas. Springer, New York 2010 (také česky Cipra, T.: Finanční a pojistné vzorce. Grada, Praha 2006).

Gerber H.U.: Lebensversicherungsmathematik. Springer-Verlag 1986 (také anglicky Life Insurance Mathematics).

Cipra, T.: Pojistná matematika: teorie a praxe. Ekopress, Praha 2006.

Cipra, T.: Penze: kvantitativní přístup. Ekopress, Praha 2012.

Cipra, T.: Penzijní pojištění a jeho výpočetní aspekty. HZ, Praha 1996.

Cipra, T.: Riziko ve financích a pojišťovnictví: Basel III a Solvency II. Ekopress, Praha 2015.

Cipra, T.: Zajištění a přenos rizik v pojišťovnictví. Grada, Praha 2004.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (04.09.2023)
Teaching methods -


Last update: T_KPMS (13.05.2013)
Requirements to the exam -

1. Possibility of written exam test: 10 questions covering the course; only one term for this test in the end of semester; a correction is possible by means of an oral exam.

2. Otherwise the oral exam with requirements corresponding to the syllabus of the course.

3. Credit from the exercise is not a condition for passing exam.

It is probable that a part of exams and exercise class credits will be possible in a distance form. It depends on the actual situation and you will be informed on all changes in time.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (30.04.2020)
Syllabus -

Multiple decrements model. Multiple life insurance. Calculation of premiums and reserves including expense loadings. Pension funds.

1. Allocation of loss to policy years. Hattendorf Theorem.

2. Technical gain.

3. Model of reserves in continuous time. Thiele differential equation.

4. Multiple state models and multiple decrements.

5. Multiple life insurance. Joint-life status. Last-survivor status. Multiple life annuities.

6. Gross premium and gross premium reserve. Zillmerisation.

7. Cash flow analysis in life insurance. Profit measures.

8. Pension insurance. Defined contribution and defined benefit pension plans.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (04.09.2023)
Entry requirements -

Basic knowledge of financial mathematics. Knowledge of mathematics of life insurance delivered in course Life Insurance 1.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (24.04.2018)
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