Modeling Insurance Claims Distribution through Combining Generalized Hyperbolic Skew-t Distribution with Extreme Value Theory

This paper examines whether combining Generalized Hyperbolic Skew-t distribution, recently introduced in the field of insurance, and Extreme Value Theory (EVT) could result in a modeling of loss function that could model central value as well as extreme value in appropriate manner.
The data used in this study are the amount of property damage and bodily injury covered under automobile liability insurance.
In order to calibrate Generalized Hyperbolic Skew-t distribution, Expectation Maximization (EM) algorithm has been used. For modeling extreme value based on Peak over Threshold approach, the Maximum Likelihood Estimation (MLE) has been applied.
Results reveal that proposed combined distribution could model the losses caused by this type of insurance in a satisfactory manner.