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

Yıl 2011, Cilt: 4 Sayı: 1, 9 - 15, 30.12.2011

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.

Kaynakça

  • G. Barnett, B. Zehnwirth, 2000, Best Estimates for Reserves, Proceedings of Casualty Actuarial Society, Vol.LXXXVII, Part 2, No.167, 245-321.
  • G. Barnett, D. Odell, B. Zehnwirth, 2008, Meaningful Intervals, Casualty Actuarial Society E-Forum, Fall 2008.
  • A. Gisler, 2006, The Estimation Error in the Chain Ladder Reserving Method:A Bayesian Approach. Astin Bulletin 36/2, 554-565.
  • A. Gisler, M.V. Wüthrich, 2007, Credibility for the Chain Ladder Reserving Method. Conference Paper, 37th. Astin Colloquium 2007, Orlando, USA.
  • C.A. Hachemeister, J.N. Stanard, 1975, IBNR Claims Count Estimation with Static Lag Functions. Astin Colloquium 1975, Portimão, Portugal.
  • 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.
  • A. Ludwig, K.D. Schmidt, 2010, Gauss-Markov Loss Prediction in a Linear Model. Casualty Actuarial Society E-Forum, Fall 2010.
  • T. Mack, 1991, A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves. Astin Bulletin 21/1, 93-109.
  • T. Mack, 1993, Distrubution-free calculation of the Standard Error of Chain Ladder Reserve Estimates, Astin Bulletin 23/2, 213-225.
  • A.E. Renshaw, 1989, Chain Ladder and Interactive Modelling (Claims Reserving and GLIM). J.Institute Actuaries 116, 559-587.
  • A.E. Renshaw, R.J. Verrall, 1998, A Stochastic Model Underlying the Chain Ladder Technique. British Actuarial J. 4/4, 903-923.
  • R. Schnieper, 1991, Separating True IBNR and IBNER Claims. Astin Bulletin 21/7, 111-127.
  • G.G. Venter, 1998, Testing the Assumptions of Age-to-age Factors. Proc. CAS, Vol. LXXXV, 807-847.
  • R.J. Verrall, 1989, A State Space Representaiton of the Chain Ladder Linear Model. J.Institute Actuaries 116, 589-609.
  • M.V. Wütrich, M. Merz, 2008, Stochastic Claims Reserving Methods in Insurance, 1-90.

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

Yıl 2011, Cilt: 4 Sayı: 1, 9 - 15, 30.12.2011

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.

Kaynakça

  • G. Barnett, B. Zehnwirth, 2000, Best Estimates for Reserves, Proceedings of Casualty Actuarial Society, Vol.LXXXVII, Part 2, No.167, 245-321.
  • G. Barnett, D. Odell, B. Zehnwirth, 2008, Meaningful Intervals, Casualty Actuarial Society E-Forum, Fall 2008.
  • A. Gisler, 2006, The Estimation Error in the Chain Ladder Reserving Method:A Bayesian Approach. Astin Bulletin 36/2, 554-565.
  • A. Gisler, M.V. Wüthrich, 2007, Credibility for the Chain Ladder Reserving Method. Conference Paper, 37th. Astin Colloquium 2007, Orlando, USA.
  • C.A. Hachemeister, J.N. Stanard, 1975, IBNR Claims Count Estimation with Static Lag Functions. Astin Colloquium 1975, Portimão, Portugal.
  • 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.
  • A. Ludwig, K.D. Schmidt, 2010, Gauss-Markov Loss Prediction in a Linear Model. Casualty Actuarial Society E-Forum, Fall 2010.
  • T. Mack, 1991, A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves. Astin Bulletin 21/1, 93-109.
  • T. Mack, 1993, Distrubution-free calculation of the Standard Error of Chain Ladder Reserve Estimates, Astin Bulletin 23/2, 213-225.
  • A.E. Renshaw, 1989, Chain Ladder and Interactive Modelling (Claims Reserving and GLIM). J.Institute Actuaries 116, 559-587.
  • A.E. Renshaw, R.J. Verrall, 1998, A Stochastic Model Underlying the Chain Ladder Technique. British Actuarial J. 4/4, 903-923.
  • R. Schnieper, 1991, Separating True IBNR and IBNER Claims. Astin Bulletin 21/7, 111-127.
  • G.G. Venter, 1998, Testing the Assumptions of Age-to-age Factors. Proc. CAS, Vol. LXXXV, 807-847.
  • R.J. Verrall, 1989, A State Space Representaiton of the Chain Ladder Linear Model. J.Institute Actuaries 116, 589-609.
  • M.V. Wütrich, M. Merz, 2008, Stochastic Claims Reserving Methods in Insurance, 1-90.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

G. Demir Ay Bu kişi benim

Murat Büyükyazıcı

Yayımlanma Tarihi 30 Aralık 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 4 Sayı: 1

Kaynak Göster

IEEE G. D. Ay ve M. Büyükyazıcı, “Türkiye zorunlu trafik sigortası dalında toplam hasar rezervi tahminlerinin hata kareler ortalaması”, JSSA, c. 4, sy. 1, ss. 9–15, 2011.