  This thesis evaluates most of the extreme mixture models and methods that
have appended in the literature and implements them in the context of finance
and insurance. The paper also reviews and studies extreme value theory, time
series, volatility clustering, and risk measurement methods in detail.
Comparing the performance of extreme mixture models and methods on different
simulated distributions shows that the method based on kernel density
estimation does not have an absolute superior or close to the best performance,
especially for the estimation of the extreme upper or lower tail of the
distribution. Preprocessing time series data using a generalized autoregressive
conditional heteroskedasticity model (GARCH) and applying extreme value mixture
models on extracted residuals from GARCH can improve the goodness of fit and
the estimation of the tail distribution.
