Ruin probability in heavy tailed risk models

Abstract

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.

Keywords

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

Kalın kuyruklı risk modellerinde iflas olasılığı

Abstract

 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.

Keywords

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

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