M7988 Models of losses in non-life insurance

Faculty of Science
Autumn 2024
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
RNDr. Radim Navrátil, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Radim Navrátil, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M7988/01: Thu 10:00–10:50 MP1,01014, R. Navrátil
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 / plans the course is directly associated with
Course objectives
The goal of the course is to show advanced methods of mathematical statistics used for modelling in non-life insurance.
Learning outcomes
After completing this course students will be able to:
(1) estimate parameters for models used in non-life insurance;
(2) model dependency of multivariate variables via kopulas;
(3) model extreme and rare events;
(4) basic concepts of Bayesian modeling.
Syllabus
  • Basic concepts of mathematical statistics - point estimates, confidence intervals, hypotheses testing.
  • Estimation methods for complete data - estimates of cumulative distribution function.
  • Parameter estimates - maximum likelihood method, method of moments, Bayesian approach.
  • Model selection - graphical methods, testing hypotheses.
  • Extreme values theory - definition and application of Pareto distribution, parameter estimates.
  • Kopulas - definition, Sklar's theorem, aplications, empirical estimates.
Literature
    recommended literature
  • KLUGMAN, Stuart A., Harry H. PANJER and Gordon E. WILLMOT. Loss models : from data to decisions. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2008, xix, 726. ISBN 9780470187814. info
Teaching methods
Lectures - gaining knowledge of statistical models used in insurance. Exercises - practical use of the methods in statistical software R.
Assessment methods
Oral exam - correctly solved project and correctly answered questions are needed to pass.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/M7988