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).
Taught in person.
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
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 - 50% of correct answers and correctly solved project are needed to pass.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
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 (Autumn 2024, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/M7988