Application of Inhomogeneous Phase-Type Distributions in Reinsurance Modelling

Specialeforsvar: Christoffer Høffding Koudahl Larsen

Titel: Application of Inhomogeneous Phase-Type Distributions in Reinsurance Modelling

Abstract: The role of the reinsurance companies is crucial for the general insurance business when larger events such as storms or earthquakes happen. This makes claim modelling a vital task for the reinsurance company to be able to assess the risks they face. The reinsurance companies work with the first-line insurers under different treaties, including the quota-share, excess-of-loss and the LCR treaty. The claims and pricing models have traditionally been based on extreme value theory and asymptotical results. We propose the inhomogeneous and homogeneous phasetype distributions as modelling choices as these distributions provide tractable formulas and properties for claims modelling. We derive new properties including the order statistics for the
inhomogeneous phase-type distribution and a way of deriving the distribution of the sum of order statistics based on phase-type distributions. The properties of these distributions are then used to show how the modelling of the different treaties can be evaluated in practice as the phase-type distributions provide the relevant tractable formulas. Especially for the claims modelling in the LCR treaty, which traditionally only can be calculated asymptotically, can now be calculated through a closed-form solution provided by the phase-type distribution.

Vejledere: Mogens Bladt, Thomas Mikosch
Censor:     Bjarne Højgaard, Spar Nord