# Content

Understanding and managing risks caused by extreme events is one of the most demanding problems of our society. In the class we consider this topic from a statistical point of view and present some of the probabilistic and statistical theory, which was developed to model and quantify extreme events. By the very nature of an extreme event there will never be enough data to predict a future risk in the classical statistical sense. However, a rather clever probabilistic theory provides us with model classes relevant for the assessment of extreme events. Moreover, specific statistical methods allow for the prediction of rare events, even outside the range of previous observations.

# Topics

• Theorem of Fisher and Tippett

• Generalized Extreme Value distribution (GED) and Generalized Pareto Distribution (GPD)

• maximum domain of attraction

• Theorem of Pickands-Balkema-de Haan

• estimation of risk measures

• Hill-estimator

• block-maxima method

• POT method

# Software

• Software for Extreme Value Analysis (Eric Gilleland)

• Statistics of Weather and Climate Extremes (Richard Katz)

# Prerequisite

The contents of the modul Wahrscheinlichkeitstheorie (Probability Theory).

# Problem classes

Lectures and problem classes will be given until July 3 2014. In general, there will be a problem class after two lectures.

Dates of problem classes:

Thursday | 24 April | 1. Problem Class |

Thursday | 8 May | 2. Problem Class |

Monday | 19 May | 3. Problem Class |

Monday | 2 June | 4. Problem Class |

Monday | 16 June | 5. Problem Class |

Thursday | 3 July | 6. Problem Class |

# Examination

There will be oral exams at the end of the semester. They are currently planned to take place on

Wednesday, 30. July 2014 and

Wednesday, 10. September 2014.

If you wish to take an exam, please sign up by entering your name and E-mail address in the lists kept by the secretary of the institute, Mrs. Tatjana Dominic (Room 5A-22 in the Allianz building / "tatjana.dominic@kit.edu"). Master students are also required to sign up online through the QISPOS system, which is **now possible**.

# References

- Beirlant, J., Goegebeur, Y., Segers, J. und Teugels, J. (2004) Statistics of Extremes. Wiley.
- de Haan, L. und Ferreira, A. (2006) Extreme Value Theory: An Introduction. Springer.
- Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.
- Embrechts, P., Klüppelberg, C. und Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer.
- McNeil, A.J.,Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques, and Tools. Princton University Press.