Analysis of Failure Sets in Fire Insurance Data

Specialeforsvar ved Nadine Wright Herløv

Titel: Analysis of Failure Sets in Fire Insurance Data

 Abstract: Extreme value theory is an important topic to many fields today. An extreme rise in seawater levels or wave heights could potentially lead to a flooding. In an insurance company, extreme claims could lead to the ruin of the company. Since extreme values imply unlikely events, only a few historical observations have been recorded, if any. This makes it difficult to predict the future with reasonable certainty using standard statistical methods. One way of studying extreme events is by analysing failure sets. Failure sets have the advantage, that they can be customised to specific situations. In the thesis, a failure set suggested by [DeHaan2006] is analysed along with the introduction of two newly constructed failure set types. Utilising the homogeneity property of the exponent measure, the failure sets can be estimated by mani-pulating the boundary of the set. This is done by dividing with a modifier c to include more observations for the estimation. The modifier c can be expressed by a radius to obtain an intuitive idea of the modification process. In this thesis, the radius tool is elaborated in two versions. Testing the Half Way Method and the Shortest Distance Method, the latter performs the best. In order to gain even more control over the failure probability estimation, the Empirical Method is designed. The method makes it possible for the statistician to choose a desired fraction of the observations to base the estimations on. In this way, the statistician ensures a sufficient amount of observations while still estimating based on the tail of the distribution. Spectral densities have great impact on the failure probabilities of a failure set, depending on the form of the set. Therefore, they are interesting to study alongside failure sets analyses. The spectral measure is based on the exponent measure, and by the homogeneity relation of the exponent measure, the spectral densities can be estimated by using a suitable radius. For this purpose, a radius tool is created. The resulting spectral densities of the fire insurance data reveal, that they have impacted some of the failure set types more than others 

Vejleder: Thomas Mikosch
Censor:   Mette M Havning