Mathematics for Life Insurance I
- Credits: 6
- Ending: Examination
- Range: 2P + 2C
- Semester: winter
- Year: 1
- Faculty of Economic Informatics
Teachers
Included in study programs
Teaching results
The aim of the course is to master the mathematical methods and actuarial techniques used in life insurance.
Knowledge
On completing the course the student should understand the terminology and master the actuarial techniques used in both the deterministic discrete and continuous approach to insurances on single lives and on more than one life.
Skills
Based on the above knowledge, students will be able to value of the premium, the assured amount and the insurance reserve for life insurance products on one and on multiple lives.
Competence
The graduate of the course will obtain knowledge and skills that can be used in the study of Mathematics for Life Insurance II, so can be used knowledge of the issue of stochastic approach to modeling in life insurance.
Indicative content
.
Support literature
1. Sekerová, V., Bilíková, M. (2005). Poistná matematika. Bratislava : Ekonóm.
2. Bilíková, M., Johanesová, M. (2008). Aktuárske výpočty pre rôzne druhy poistenia m-tice osôb. Bratislava : Ekonóm.
3. Bilíková, M. (2003). Spojité metódy v poistnej matematike. Bratislava : Ekonóm.
4. Promislow, S. D. (2015). Fundamentals of Actuarial Mathematics. United Kingdom: John Wiley & Sons.
5. Dickson, D. C. M., Hardy, M. R. & Waters, H. R. (2009). Actuarial Mathematics for Life Contingent Risks. New York: Cambridge University Press.
Syllabus
1. Actuarial basis, basic principles of life insurance, commutation functions, pure endowment, value of basic annuities. 2. Value of special annuities. Value of basic and special insurances on death, endowment assurance. 3. Regular net premium, insurance paid only regularly, generalised form of the relationship for calculating the net premium. 4. Gross premium. English and Germany approach to gross premium. 5. Net premium reserve, prospective and retrospective calculation of the net reserve. Risk and investment part of premium. 6. Zillmer reserve, reserve for expenses, gross premium reserve, surrender and alteration of policies. Surplus and profit of insurer. 7. Continuous methods in life insurance: force of mortality. Relationships between force of mortality and mortality table functions. Laws of mortality. 8. Level annuities paid m-times a year and their approximation. Continuous annuities. 9. Assurances paid immediately on death. Further continuous assurances. Approximation of continuous by discrete assurances. Continuous insurance reserves. 10. Insurance of more than one person, basic terms, joint lives. Complete intensity and joint-life insurances. 11. Law of equal aging. State to last death, state of exactly r lives alive, state of at least r lives alive - probability, insurances. Z-method. 12. Compound states. Time interval between deaths. Reversionary annuities. 13. Regular premiums and reserves for insurances on more than one life and reversionary annuities.
Requirements to complete the course
30 % activities in tutorials, completion of given tasks and passing of semester written work (written test),
40 % written part of the exam,
30 % oral part of the exam.
Student workload
Total study load (in hours): 156 hours
26 hours attendance at lectures,
26 hours participation in tutorials,
26 hours preparation for tutorials,
26 hours preparation for semester written work,
56 hours preparation for exam.
Language whose command is required to complete the course
slovak
Date of approval: 10.02.2023
Date of the latest change: 15.05.2022