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PřF:M7987 Statist. models of life insur. - Course Information

## M7987 Statistical models of life insurance

**Faculty of Science**

Autumn 2018

**Extent and Intensity**- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)

Mgr. Markéta Janošová (seminar tutor) **Supervisor**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Contact Person: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 17. 9. to Fri 14. 12. Tue 8:00–9:50 M4,01024
- Timetable of Seminar Groups:

*M. Janošová* **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 the course is directly associated with**- Finance Mathematics (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Statistics and Data Analysis (programme PřF, N-MA)

**Course objectives**- The main goal of the course is to become familiar with some basic probabilistic and statistical models in life insurance of one and more lives, multi-state models, and models in health and pension insurance; to highlight the relationship with survival analysis; to implement these techniques into R language and to be able to apply them to real data.
**Learning outcomes**- Student will be able:

- to understand principles of likelihood and statistical inference for (un)censored life-time data;

- to select suitable probabilistic and statistical model in statistical inference for (un)censored life-time data;

- to build up and explain suitable simulation study for selected statistical test or confidence for (un)censored life-time data;

- to build up and explain suitable statistical test for (un)censored life-time data;

- to apply statistical inference on real for (un)censored life-time data (life, health and pension insurance of one and two lives);

- to implement methods of statistical inference for (un)censored life-time data in R. **Syllabus**- Survival characteristics and their actuarial notation - distribution function, survival function, density, risk function, expected value and variance of survival time, mean residual life.
- Selected models of probability distributions from the generalized gamma family and related distributions - exponential distribution, extreme value distribution, Weibull distribution, log-logistic and lognormal distribution, gamma and generalized gamma distribution.
- Likelihood functions, point and interval estimates of parameters of selected distributions, statistical inference for uncensored and censored data, goodness of fit tests, selection of appropriate distribution, testing of statistical hypotheses by Wald principle, likelihood ratio and score principle.
- Parametric regression models in survival analysis for uncensored and censored data (one, two, and multiple samples).
- Gompertz, Makeham, and generalized Gompertz-Makeham distribution. Mortality tables. Life insurance for one or more lives, present value, mean value, second moment and variance of the present value of life, health and pension insurance of one and two lives. Implementation of methods in R and application to real data.

**Literature**- DICKSON, D. C. M., Mary HARDY and H. R. WATERS.
*Actuarial mathematics for life contingent risks*. 2nd ed. Cambridge: Cambridge University Press, 2013. xxi, 597. ISBN 9781107044074. info - BOWERS, Newton L.
*Actuarial mathematics*. 2nd ed. Schaumburg, Ill.: Society of Actuaries, 1997. xxvi, 753. ISBN 0938959468. info - GERBER, Hans U.
*Life insurance mathematics*. Edited by Samuel H. Cox. 3rd ed. Zurich: Springer, 1997. xvii, 217. ISBN 354062242X. info

- DICKSON, D. C. M., Mary HARDY and H. R. WATERS.
**Teaching methods**- Lectures, practicals.
**Assessment methods**- Homework, oral exam.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2018/M7987