Mathematics for Life Insurance II

  • Credits: 5
  • Ending: Examination
  • Range: 2P + 2C
  • Semester: summer
  • Year: 1
  • Faculty of Economic Informatics

Teachers

Included in study programs

Actuarial Science

Teaching results

The aim of the course is to provide knowledge of the stochastic approach to modeling life insurance products. The valuation of premiums, reserves and life insurance risks is performed using appropriately selected functions of a random variable. The graduate of the course will obtain:
Knowledge and understanding
- knowledge of modeling risks, premiums and reserves in life insurance using the random variable function,
- knowledge of mortality models and modeling the mortality risk,
- knowledge of modeling the stochastic interest rate.
Skills
- students will be able to value insurance premiums and reserves based on a stochastic approach,
- students will be able to express the loss or profit of the insurance company and use it in actuarial calculations.
Competence
- knowledge and skills that can be used to expand knowledge of the issue of the stochastic approach to modeling in life insurance.

Indicative content

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Support literature

1. Šoltésová, T. (2019). Aktuárske modelovanie v životnom poistení. Bratislava: Vydavateľstvo Letra Edu.
2. Dickson, D. C. M., Hardy, M. R. & Waters, H. R. (2009). Actuarial Mathematics for Life Contingent Risks. New York: Cambridge University Press.
3. Olivieri, A., Pitacco, E. (2015). Introduction to insurance mathematics: technical and financial features of risk transfers. New York: Springer.
4. Promislow, S. D. (2014). Fundamentals of actuarial mathematics. John Wiley & Sons.

Syllabus

1. Future lifetime random variable (RV) at birth, its basic functions. Future lifetime RV for a life aged x, force of mortality, probability density, expectation of life. 2. The curate future lifetime. Definition of mortality tables based on the stochastic approach. 3. The fractional age assumptions for the future lifetime RV for a life aged x between integer ages. 4. Continuous insurances as functions of the future lifetime RV for a life aged x, their means and standard deviations. 5. Continuous annuities as functions of the future lifetime RV for a life aged x, their means and standard deviations. 6. Discrete insurances as functions of RV curtate future lifetime, their means and standard deviations. 7. Generalization of basic types of insurances and recurrent formulas in a stochastic approach. 8. The stochastic approach to life insurance on m lives: joint life, state to last death. 9. The stochastic approach to insurances on m lives: contingent insurances and reversionary annuities. 10. Future loss RV of an insurer from a specified policy and its use in actuarial calculations. 11. The using a stochastic approach to a calculation of premiums, various criteria for the calculation. 12. Reserves in a stochastic approach. The death strain, the profit from mortality. 13. Stochastic modeling of the mortality risk and the interest rate risk.

Requirements to complete the course

The semester work - written test - 30%,
Written part of the exam - 40%
Oral part of the exam - 30%

Student workload

Total study load (in hours):
Participation in lectures - 20
Participation in exercises - 20
Preparation for exercises – 20
Preparation for the semester work - 20
Preparation for the final exam - 50
Total load - 130

Language whose command is required to complete the course

slovak

Date of approval: 10.02.2023

Date of the latest change: 15.05.2022