Η γενικευμένη κατανομή ακραίων τιμών και εφαρμογές της στον αναλογισμό

Τατσή, Μαριάννα Δ.

The generalized extreme value distribution and its applications in actuarial science

Master Thesis

Author

Τατσή, Μαριάννα Δ.

Date

2015-06

Abstract

In this thesis we offer a brief presentation of extreme value theory and discuss its usefulness in Insurance and extreme events. An extensive description to parameter estimation methods for extreme value distributions i.e. Gumbel, Frechet, Weibull is given along with numerical comparison of the efficiency of the estimators by the aid of a simulation study. Generalized Extreme Value distribution (GEV) is covered as well and an illustration is provided on how it can be adapted to real loss data. In addition we calculate sample risk measures Value-at-Risk and Expected Shortfall and compare them to the corresponding measures of the estimated distribution. Finally, we conducted an estimation of the aggregate loss function using a Monte Carlo simulation to forecast risk measures and analyze their sensitivity against different confidence levels.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διοικητική Κινδύνου

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

120

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/9221

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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