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Mathematics of Life Insurance 2 - NMFP432

Title:	Matematika životního pojištění 2
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Tomáš Cipra, DrSc.
Teacher(s):	prof. RNDr. Tomáš Cipra, DrSc. RNDr. Petr Vejmělka
Class:	M Mgr. FPM M Mgr. FPM > Povinně volitelné
Classification:	Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Interchangeability :	{Life Insurance 2 - lecture as well exercise class}
Incompatibility :	NMFM406, NMFM416
Pre-requisite :	NMFP407
Is incompatible with:	NMFM406, NMFM416
Is pre-requisite for:	NMFP558
Is interchangeable with:	NMFM416, NMFM406

Opinion survey results Examination dates Noticeboard

Annotation -

Decomposition of loss of insurer into particular years. Technical gain. Multiple decrements models. Multiple life insurance. Calculation of premiums and reserves including expense loadings. Pension insurance and pension funds.

Last update: Branda Martin, doc. RNDr., Ph.D. (05.12.2020)

Aim of the course -

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

Last update: Zichová Jitka, RNDr., Dr. (17.05.2024)

Course completion requirements -

Course credit requirements:

1) gaining at least 70 % of the total points from 2 homework assignments with solutions sent by deadlines during the semester,

2) gaining at least 70 % of the total points from the final test written at the end of the semester.

One regular and one retake term will be available to pass the final test.

The nature of the requirements precludes the possibility of additional attempts to obtain the course credit.

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.

Last update: Vejmělka Petr, RNDr. (27.02.2024)

Literature -

Gerber H.U.: Life Insurance Mathematics. Springer, Berlin 1997.

Cipra, T.: Financial and Insurance Formulas. Springer, New York 2010.

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

Cipra, T.: Finanční a pojistné vzorce. Grada, Praha 2006.

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

Cipra, T.: Practical Guide to Financial and Insurance Mathematics. Ekopress, Praha 2020.

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

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

Last update: Cipra Tomáš, prof. RNDr., DrSc. (04.12.2020)

Teaching methods -

Lecture + exercises.

Last update: Zichová Jitka, RNDr., Dr. (13.05.2022)

Syllabus -

1. Decomposition of loss of insurer into particular years. Hattendorf's theorem

2. Technical gain.

3. Models in continuous time. Thiel's differential equation.

4. Multiple decrements models.

5. Multiple life insurance.

6. Calculation of premiums and reserves including expense loadings. Zillmerisation.

7. Pension insurance and pension funds.

Last update: Cipra Tomáš, prof. RNDr., DrSc. (04.12.2020)