Μοντελοποίηση ασφαλιστικών απαιτήσεων : κατασκευή κατανομών με βαριές ουρές μέσω μετασχηματισμού της κατανομής Weibull
Modeling insurance claims : heavy tailed distributions generation by transforming the Weibull distribution
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Keywords
Heavy tailed ; WeibullAbstract
It is well known that the severity of insurance claims follows heavy-tailed distributions, a property that classical distributions (normal, exponential, etc.) do not possess. For this reason, particular attention has been paid to the creation of new families of distributions that can satisfactorily approximate heavy-tailed data and to the study of their properties.
In this thesis, we first report some basic properties of heavy-tailed distributions. Then, we present the Weibull distribution, which belongs to the heavy-tailed distribution family.
Next, we present a transformation of the Weibull distribution which provide a better fit to heavy-tailed data, such as insurance claims, and compare the risk measures Value at Risk (VaR) and Expected Shortfall (TVaR/Expected Shortfall) between the standard Weibull distribution and its transformation.
Finally, the efficiency of these techniques is investigated on simulated data and then an application to real insurance loss data is conducted.