Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Probability Theory and Statistics

Code

aringa1u0um17em

Title

Price fluctuations (l)

Usual semester

Spring

Published semester

2025/26/2

ECTS

6

Language

hu

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyse mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

Multivariate stable distributions. Extreme-value distributions, max-domains of attraction Parameter estimation, confidence intervals in extreme-value  models Multivariate extreme-value distributions, Peaks over threshold models  in one dimension Multivariate POT models, point processes Bootstrap Elliptic distributions,copulas with applications Goodness of fit for copulas, problems in higher dimensions Random matrices, portfolio optimisation and instability, risk measures, , ARCH-GARCH models, legislation questions The crisis in 2007-2009 and its effect, stress testing, machine learning Necessary prior knowledge: BSc level probability theory

Assessment method

written exam

Bibliography

lecture notes

Recommended bibliography

Chambers, J.M., Mallows, C. and Stuck, B.W.: A method for simulating stable random variable (1976) Michael, P.: The stabilized probability plot (1983) Nolan, J. P.: Modeling financial data with stable distributions (2005) Nolan, J. P.: Stable distributions (2009)

Programmes of the course