Η γενικευμένη κατανομή ακραίων τιμών και εφαρμογές της στον αναλογισμό
The generalized extreme value distribution and its applications in actuarial science
Τατσή, Μαριάννα Δ.
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.