Mean Square Error of Total Claims Reserve Prediction in the Mandatory Traffic Insurance of Turkey

Öz

In this study, claims payments which will be made over the years gradually in the future and loss reserves

which are total of these claims payments will be predicted by using chain ladder method. Also, estimators that

were introduced in the studies of Wüthrich and Merz (2008) and Mack (1993) will be given for the mean

square error of the ultimate claim reserve. In application part of this study, the cumulative claims triangle data

of 22 companies serving in the mandatory traffic insurance for the 2004 – 2010 period are used. Two

aforementioned estimators were applied and mean square error predictions and variational coefficients were

computed for 22 companies. Finally, average variational coefficient for total claims reserves for any company

working in this insurance sector was calculated. Thus, an opportunity will be given to the insurance companies

for making a stochastical assessment of the total claim reserve estimate’s quality.

Anahtar Kelimeler

• Prediction of loss reserve,chain-ladder method,mean square error,mandatory traffic insurance.

Türkiye zorunlu trafik sigortası dalında toplam hasar rezervi tahminlerinin hata kareler ortalaması

Öz

 Bu çalışmada, gelecek yııllarr boyunca kademeli yapılacak  olan hasar ödemeleri ve bu ödemelerin toplamından

oluan hasar rezervleri, zincir merdiven yöntemi ile tahmin edilmiştir. Ayrıca bu yöntem ile elde edilen hasar

rezervlerinin hata kareler ortalaması için Wüthrich ve Merz (2008)’in çalmasnda ortaya konan koşullu

tahmin edici ile Mack (1993)’in çalmasnda ortaya konan tahmin edici anlatlmtr. Uygulama ksmnda,

Türkiye’de zorunlu trafik sigortas dalnda hizmet veren 22 sigorta irketinin 2004 – 2010 yllar için birikimli

hasar miktar gelişim üçgeni verileri kullanlmtr. 22 irketin tamamna, söz konusu iki tahmin edici

uygulanarak hata kareler ortalamalar hesaplanm, zorunlu trafik sigortas sektöründeki herhangi bir irket

için toplam rezerv miktarnn ortalama de2iim katsays elde edilmitir. Bu de2erin tahmin edilmesiyle,

sigorta irketlerinin zorunlu trafik sigortas hasar rezervi tahminlerine ilikin stokastik bir de2erlendirme

yapmalarna olanak sa2lanm olmaktadr.

Anahtar Kelimeler

• Hasar rezervi tahmini, zincir merdiven yöntemi, hata kareler ortalamas , zorunlu trafik sigortas

Kaynakça

1. G. Barnett, B. Zehnwirth, 2000, Best Estimates for Reserves, Proceedings of Casualty Actuarial Society, Vol.LXXXVII, Part 2, No.167, 245-321.
2. G. Barnett, D. Odell, B. Zehnwirth, 2008, Meaningful Intervals, Casualty Actuarial Society E-Forum, Fall 2008.
3. A. Gisler, 2006, The Estimation Error in the Chain Ladder Reserving Method:A Bayesian Approach. Astin Bulletin 36/2, 554-565.
4. A. Gisler, M.V. Wüthrich, 2007, Credibility for the Chain Ladder Reserving Method. Conference Paper, 37th. Astin Colloquium 2007, Orlando, USA.
5. C.A. Hachemeister, J.N. Stanard, 1975, IBNR Claims Count Estimation with Static Lag Functions. Astin Colloquium 1975, Portimão, Portugal.
6. Hazine Müste arl 2 ’n n Aktüeryal Zincirleme Merdiven Metoduna Ali kin 20.09.2010 tarih ve 2010/12 say l Genelgesi. http://www.hazine.gov.tr/irj/portal/anonymous?NavigationTarget=navurl://3c71afc847262b8a5d4568ffcf28 d0df&LightDTNKnobID=1890605360.
7. A. Ludwig, K.D. Schmidt, 2010, Gauss-Markov Loss Prediction in a Linear Model. Casualty Actuarial Society E-Forum, Fall 2010.
8. T. Mack, 1991, A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves. Astin Bulletin 21/1, 93-109.

9. T. Mack, 1993, Distrubution-free calculation of the Standard Error of Chain Ladder Reserve Estimates, Astin Bulletin 23/2, 213-225.
10. A.E. Renshaw, 1989, Chain Ladder and Interactive Modelling (Claims Reserving and GLIM). J.Institute Actuaries 116, 559-587.
11. A.E. Renshaw, R.J. Verrall, 1998, A Stochastic Model Underlying the Chain Ladder Technique. British Actuarial J. 4/4, 903-923.
12. R. Schnieper, 1991, Separating True IBNR and IBNER Claims. Astin Bulletin 21/7, 111-127.
13. G.G. Venter, 1998, Testing the Assumptions of Age-to-age Factors. Proc. CAS, Vol. LXXXV, 807-847.
14. R.J. Verrall, 1989, A State Space Representaiton of the Chain Ladder Linear Model. J.Institute Actuaries 116, 589-609.
15. M.V. Wütrich, M. Merz, 2008, Stochastic Claims Reserving Methods in Insurance, 1-90.