# 401-3919-60L An Introduction to the Modelling of Extremes

Semester | Spring Semester 2017 |

Lecturers | P. Embrechts |

Periodicity | yearly course |

Language of instruction | English |

Abstract | This course yields an introduction into the MATHEMATICAL THEORY of one-dimensional extremes, and this mainly from a more probabilistic point of view. |

Objective | In this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models. They learn to do probabilistic modelling of extremes in one-dimensional data. The probabilistic key theorems are the Fisher-Tippett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively. |

Content | - Introduction to rare or extreme events - Regular Variation - The Convergence to Types Theorem - The Fisher-Tippett Theorem - The Method of Block Maxima - The Maximal Domain of Attraction - The Fre'chet, Gumbel and Weibull distributions - The POT method - The Point Process Method: a first introduction - The Pickands-Balkema-de Haan Theorem and its applications - Some extensions and outlook |

Lecture notes | There will be no script available, students are required to take notes from the blackboard lectures. The course follows closely Extreme Value Theory as developed in: P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer. |

Literature | The main text on which the course is based is: P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer. Further relevant literature is: S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer. S. I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer. |