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.
Kaynakça
- [1] Asmussen, S., 2000, Ruin probabilities, Advanced Series on Statistical Science and Applied Probability Vol.2, World Scientific Publishing, Singapore, 385p.
- [2] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987, Regular variation, Cambridge University Press, Cambridge.
- [3] Chistyakov, V.P., 1964, A theorem on sums of independent positive random variables and its applications to branching random processes, Theory probability Application 9, pp 640-649.
- [4] Embrechts, P., Goldie, C.M., 1982, On convolution tails, Stochastic Processes Applied 13, pp 263-278.
- [5] Embrechts, P., Klüppelberg C., Mikosch T., 2001, Modelling Extremal Events for Insurance and Fnance, Applications of Mathematics Stochastic Modelling and Applied Probability 33 , Springer, 648p.
- [6] Goldie, C. M., Klüppelberg C., 1998, Subexponential Distributions, A practical guide to heavy tails: statistical techniques and applications, pp 435-460.
- [7] Klugman, S.,A., Panjer H.H., Willmot G.,E., 2008, Loss models from data to decisions, Third Edition, John Wiley and Sons, New Jersey, 726p.
- [8] Klüppelberg, C., 1988, Subexponential distributions and integrated tails, Journal of Applied Probability,Vol 25,No:1,pp 132-14.1
- [9] Mo, K.C.K., 2002, Ruin probabilities with dependent claims, Actuarial Studies, Faculty of Commerce and Economics, University of New South Wales, 50p.
- [10] Rolski T., Schmidli H., Schmidt V., Teugels J., 1999, Stochastic processes for Insurance and Finance, Wiley Series in Probability and Statstics, John Wiley and Sons, England, 654p.
- [11] Sigman K., 1999, Appendix: A primer on heavy-tailed distributions, Queueing Systems 33, pp 261-275
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
- [1] Asmussen, S., 2000, Ruin probabilities, Advanced Series on Statistical Science and Applied Probability Vol.2, World Scientific Publishing, Singapore, 385p.
- [2] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987, Regular variation, Cambridge University Press, Cambridge.
- [3] Chistyakov, V.P., 1964, A theorem on sums of independent positive random variables and its applications to branching random processes, Theory probability Application 9, pp 640-649.
- [4] Embrechts, P., Goldie, C.M., 1982, On convolution tails, Stochastic Processes Applied 13, pp 263-278.
- [5] Embrechts, P., Klüppelberg C., Mikosch T., 2001, Modelling Extremal Events for Insurance and Fnance, Applications of Mathematics Stochastic Modelling and Applied Probability 33 , Springer, 648p.
- [6] Goldie, C. M., Klüppelberg C., 1998, Subexponential Distributions, A practical guide to heavy tails: statistical techniques and applications, pp 435-460.
- [7] Klugman, S.,A., Panjer H.H., Willmot G.,E., 2008, Loss models from data to decisions, Third Edition, John Wiley and Sons, New Jersey, 726p.
- [8] Klüppelberg, C., 1988, Subexponential distributions and integrated tails, Journal of Applied Probability,Vol 25,No:1,pp 132-14.1
- [9] Mo, K.C.K., 2002, Ruin probabilities with dependent claims, Actuarial Studies, Faculty of Commerce and Economics, University of New South Wales, 50p.
- [10] Rolski T., Schmidli H., Schmidt V., Teugels J., 1999, Stochastic processes for Insurance and Finance, Wiley Series in Probability and Statstics, John Wiley and Sons, England, 654p.
- [11] Sigman K., 1999, Appendix: A primer on heavy-tailed distributions, Queueing Systems 33, pp 261-275
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 23 Temmuz 2011 |
| Yayımlandığı Sayı | Yıl 2011 Cilt: 4 Sayı: 2 |