SubjectsSubjects(version: 964)
Course, academic year 2024/2025
   Login via CAS
Risk Theory 1 - NMFP503
Title: Teorie rizika 1
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information: https://dl1.cuni.cz/course/view.php?id=15603
Guarantor: RNDr. Lucie Mazurová, Ph.D.
Teacher(s): Mgr. Ing. Pavel Kříž, Ph.D.
RNDr. Lucie Mazurová, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
Classification: Mathematics > Financial and Insurance Math.
Is incompatible with: NMFM503
In complex interchangeability with: NMFM503
Annotation -
Introduction to extreme value theory. Block maxima method. Analysis of threshold exceedances. Copulas. Sklar theorem and multivariate data modeling. Dependence measures.
Last update: Branda Martin, doc. RNDr., Ph.D. (13.12.2020)
Course completion requirements -

Requirements to successfully pass the practicals: To complete the test at the end of semester with at least 60 % of points achieved. The test contains exercises similar to those solved during the classes.

Last update: Mazurová Lucie, RNDr., Ph.D. (03.10.2024)
Literature -

A.J. McNeil, R. Frey, P. Embrechts: Quantitative Risk Management. Princeton University Press, 2005.

P. Embrechts, C. Klüppelberg, T. Mikosch: Modeling Extremal Events for Insurance and Finance. Springer, 1997.

R.B. Nelsen: An Introduction to Copulas. Springer, 2006.

Last update: Branda Martin, doc. RNDr., Ph.D. (13.12.2020)
Teaching methods -

Lecture + exercises.

Last update: Zichová Jitka, RNDr., Dr. (09.05.2023)
Requirements to the exam -

Oral exam with written preparation. Requirements for the exam consist of the entire extent of the lecture.

Last update: Mazurová Lucie, RNDr., Ph.D. (03.10.2024)
Syllabus -

1. Extreme value distributions. Block maxima analysis. Generalized Pareto distribution. Analysis of threshold exeedances.

2. Copulas. Sklar theorem. Comonotonicity and countermonotonicity. Implicit copulas. Bivariate archimedean copulas.

3. Dependence measures. Coefficients of rank correlation. Coefficients of tail dependence.

4. Estimating copulas from data. Simulation of copulas.

Last update: Mazurová Lucie, RNDr., Ph.D. (12.12.2020)
Entry requirements -

Probability distribution and its characteristics, convergence of sequences of random variables, random vectors, multivariate distributions, marginal and conditional distributions. Maximum likelihood method.

Last update: Mazurová Lucie, RNDr., Ph.D. (12.06.2024)
 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html