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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 2023
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
Teaching methods:	full-time

Guarantor:	RNDr. Lucie Mazurová, Ph.D. doc. RNDr. Martin Branda, 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

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Annotation -

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

Introduction to extreme value theory. Block maxima method. Analysis of threshold exceedances. Copulas. Sklar theorem and multivariate data modeling. Dependence measures.

Literature -

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

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.

Teaching methods -

Last update: RNDr. Jitka Zichová, Dr. (09.05.2023)

Lecture + exercises.

Syllabus -

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

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.