Ruin probability in heavy tailed risk models

Yıl 2011, Cilt: 4 Sayı: 2, 39 - 56, 23.07.2011

Başak Bulut , Cenap Erdemir

Öz

In this study, detailed information about heavy tailed distributions and the )ts sub-classes are revieved and the

conditions necessary for any distribution to belonging to one of these special classes of distributions are

explained. It is showed that how the ruin probabilities of a risk process that includes heavy tailed claim severity

amounts, can be calculated with theoretical justifications. An application is provided by using compulsory

traffic insurance data in Turkey in Matlab programming language. It is investigated if the loss severities can be

categorized under the heavy-tailed distribution and also the relevant sub-categorized of the distribution is

determined,too. Moreover, ruin probabilities are calculated in terms of different initial surplus and safety

factors by analyzing the risk process for this particular time.

Anahtar Kelimeler

Heavy-tailed distributions, Risk process, Ruin probability, Sub-exponential distributions.

Kalın kuyruklı risk modellerinde iflas olasılığı

Öz

 Bu
çalışmada, hasar tutarlarının
kalın kuyruklu dağılım
yapısına
uyup uymadığı, bu dağlım
yapısının
koşulları incelenerek
araştırılmıştır. Kalın kuyruklu dağılım
 yapısına
sahip risklerin, risk süreci ve iflas olasılıkları
üzerindeki etkisi teorik ispatlar eşliğinde
açıklanmaya çalışılmıştır.
Matlab yazılımında
geliştirilen program
sayesinde, Türkiye Trafik Sigortası veri
kümesi kullanılarak, hasar
büyüklüklerinin kalın kuyruklu dağılıma
uyup uymadığı sorgulanmış
, uyması halinde ise hangi
alt sınıfa
dahil olduğu araştırılmıştır.
Ayrıca belirlenen dönem
için risk süreci incelemesi yapılarak,
çeşitli sermaye miktarı
ve güvenlik yükleme faktörlerine bağlı  olarak iflas olasılıkları  hesaplanmıştır.

Anahtar Kelimeler

Kal)n kuyruklu da*)l)mlar, Risk süreci, %flas olas)l)*), Alt-üstel da*)l)mlar

Kaynakça

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