Fuzzy pricing of high excess loss layer when modeling the tail with generalized Pareto distribution

Öz

Good estimates for the tails of loss severity distributions are essentials for pricing or positioning high-excess

loss layers (in reinsurance). Extreme value theory (EVT) provides a framework to formalize the study of

behaviour in the tails of loss severity distributions. In EVT, the excess losses over a high threshold are

modelled using generalized Pareto distribution (GPD). In any data analysis, there are various layers of

uncertainty such as parameter and/or model uncertainty. These uncertainities are magnified in extreme value

analysis. The aim of this study is to obtain fuzzy price for high excess loss layer when GPD provides good

fitting to the tail of claim data. For this purpose, parameters of GPD are estimated using Buckley’s approach

Anahtar Kelimeler

• Buckley’ s approach,Extreme value theory,Fuzzy parameter estimation,Fuzzy pricing for high excess of loss layer,Generalized Pareto distribution.

Kuyruk bölgesi genelleştirilmiş Pareto dağılım ile modellendiğinde hasar fazlasının bulanık fiyatlandırması

Öz

 Reasüransta, hasar şiddeti dağılımlarının kuyruk bölgesinin doğru tahmini fiyatlandırma ve hasar fazlasının belirlenmesinde önemlidir. Hasar şiddeti dağılımlarının kuyruk bölgesinin modellenmesinde Uç Değer Teorisinden yararlanılmaktadır. Uç Değer Teorisinde, oldukça yüksek bir eşik değerini aşan hasarlar Genelleştirilmiş Pareto dağılımı kullanılarak modellenmektedir.

Herhangi bir veri analizinde, parametre ve/veya model belirsizliği gibi çeşitli belirsizlikler söz konusudur. Uç değer analizinde, bu belirsizlikler daha da artmaktadır. Zadeh [33] belirsizliğin üstesinden gelmek için bulanık mantığı önermiştir. Bu çalışmada, Buckley’ in yaklaşımı kullanarak Genelleştirilmiş Pareto Dağılımının parametrelerini tahmin edilmiş; bu parametre tahminleri kullanılarak hasar fazlasının bulanık fiyatlandırması elde edilmiştir.

Anahtar Kelimeler

• Buckley yaklaşımı, Bulanık parametre tahmini, Genelleştirilmiş Pareto dağılımı, Hasar fazlasının bulanık fiyatlandırması, Uç değer teorisi

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