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COMPARISON OF THE PERFORMANCE OF SOME LOSS RESERVING METHODS WITH SIMULATION

Year 2014, Volume: 15 Issue: 1, 15 - 31, 05.05.2015
https://doi.org/10.18038/btd-a.74130

Abstract

Since knowing future losses precisely could not be possible, insurer should allocate an adequate reserve in the loss process. For this purpose, insurer needs to select a suitable reserving method which estimates the expected liabilities truely. It is possible to choose the most suitable reserve method by carrying out performance tests. The performance of a method can be measured by the deviation between the estimated and the actual reserve. In this study, the loss development triangles (upper-left and lower-right triangles) are generated by using four simulation methods: random reporting factor method,  random  backward  development  factor  method,  indiviual  losses  with  changing  severity method  and  Pentikäinen  and  Rantala  method.  By  using  the  simulated  upper-left  triangles,  the estimated  total reserves and the  estimated loss reserves for each  accident year are obtained  with the chain  ladder  (CL)  method,  the  Bühlmann  complementary  loss  ratio  (BCLR)  method  and  three different regression models. The closeness of loss reserve estimations to actual loss reserves is tested by the performance criteria

References

  • Bickerstaff D. R. (1972). Automobile Collision Deductibles and Repair Cost Groups: The Lognormal Model, Proc. CAS 59, 68-102.
  • Boles T., Staudt A. (2010). On the Accuracy of Loss Reserving Methodology, CAS E- Forum Fall 2010, 43-104.
  • Bradu D., Mundlak Y. (1970). Estimation in Lognormal Lineer Models, JASA Vol. 6, 198-211.
  • Bühlmann H. (1983). Estimation of IBNR Reserves by The Methods of Chain- Ladder, Cape-Cod, and Complementary Loss Ratio, International Summer School 1983, Unpublished.
  • Dropkin L. B. (1964). Size of Loss Distributions in Workmen’s Compensation Insurance, Proc. CAS 51, 198-242.
  • England P. D., Verrall R. J. (2002). Standard Errors of Prediction in Claims Reserving: A Comparison of Methods, General Insurance Colloquium, Actuaries, Vol. 1, 459-478. & Institute of
  • Finney D. J. (1941). On the Distribution of a Variate Whose Logarithm is Normally Distributed, JRSS Suppl. 7, 155-161.
  • Friedland J. (2009). Estimating Unpaid Claims using Basic Techniques, CAS-FCAS, KPMG LLP, Version II.
  • Hewitt C. C. (1966). Distribution by Size of Risk-A Model, Proc. CAS 53, 106-115.
  • Jing Y., Lebens J., Lowe S. (2009). Claim Reserving: Performance Testing and The Control Cycle, CAS: Variance Advancing The Science of Risk, Vol. 3 Issue 2. Khury C. K. (1980). Loss Reserves: Performance Standards , Proc. CAS 67, 1- 21.
  • Klugman S. A., Panjer H. H., Willmot G. E. (2004). Loss Models: From Data to Decisions, Willey&Sons Ltd. Edition, John
  • Mack T. (1999). The Standard Error of Chain- Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor, ASTIN Bulletin 29, 361-366.
  • Narayan P., Warthen, T. V. (2000). A Comparative Study of The Performance of Loss Reserving Methods Through Simulation: Journal of Actuarial Practice, Vol. 8. Patrik G. (1980). Estimating Casualty
  • Insurance Loss Amount Distributions,
  • Proc. CAS 67, 57-109.
  • Pentikäinen T., Rantala J. (1992). A Simulation Procedure Claims Reserving Methods, ASTIN Bull, Vol. 22, No. 2, 191-216. Different
  • Renshaw A. E., Verrall R. J. (1998). A Stochastic Model Underlying The Chain- Ladder Technique, British Actuarial Journal, Vol. 4, 903-923.
  • Rollins J. W. (1997). Performance Testing Aggregate and Structural Reserving Methods: A Simulation Approach, CAS Forum Summer 1997, Vol. 1, 137-173.
  • Schmidt K. D., Zocher M. (2008). The Bornhuetter-Ferguson Principle, CAS: Variance Advancing The Science of Risk, Vol. 3 Issue 2.
  • Stanard J. N. (1985). A Simulation Test of Prediction Errors of Loss Reserving Techniques, CAS Proceedings May 1985, Vol. 72, 124-148.
  • Verrall R. J. (1991). On The Unbiased Estimation of Reserves from Loglinear Models, Insurance: Mathematics and Economics, 10, 1, 75-80.
  • Verrall R. J. (1994). Statistical Methods for The Chain Ladder Technique, CAS Forum Spring 1994, 393-446.
  • Wiser R. F. (2001). Loss Reserving, Revised and Updated By Jo Ellen Cockley and Andrea Gardner, In: Foundations of Casualty Actuarial Science, New York, 197-285
  • Wüthrich M. V, Merz M. (2008). Stochastic Claims Reserving Methods in Insurance, John Willey&Sons Ltd.  

BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI

Year 2014, Volume: 15 Issue: 1, 15 - 31, 05.05.2015
https://doi.org/10.18038/btd-a.74130

Abstract

Gelecekte ortaya çıkabilecek hasarların miktarı bilinemeyeceğinden, hasar sürecinde sigortacının yeterli rezerv ayırması, bunun için de beklenen yükümlülüğünü doğru tahmin edecek bir rezerv yöntemi seçmesi gerekmektedir. Performans testleri kullanılarak en uygun hasar rezerv yönteminin seçilmesi mümkündür. Bir yöntemin performansı, rezervin tahmin edilen değeri ile gerçekleşen değeri arasındaki sapma ile ölçülebilmektedir. Bu çalışmada, hasar gelişim üçgenleri (sol-üst ve sağ-alt üçgenler) rastgele bildirilme faktörü yöntemi, rastgele geriye doğru gelişim faktörü yöntemi, değişen tutarlı bireysel hasarlar yöntemi ve Pentikäinen ve Rantala yöntemi olmak üzere dört farklı benzetim yöntemiyle üretilmiştir. Benzetimi yapılan sol-üst üçgenler kullanılarak zincir merdiven (ZM) yöntemi, Bühlmann’ın tamamlayıcı hasar oranı (BTHO) yöntemi ve üç farklı regresyon modeli ile toplam hasar rezerv tahminleri ve her bir kaza yılına ilişkin hasar rezerv tahminleri elde edilmiştir. Hasar rezerv tahminlerinin gerçekleşen hasar rezervlerine yakınlığı performans ölçütleri yardımıyla test edilmiştir.

References

  • Bickerstaff D. R. (1972). Automobile Collision Deductibles and Repair Cost Groups: The Lognormal Model, Proc. CAS 59, 68-102.
  • Boles T., Staudt A. (2010). On the Accuracy of Loss Reserving Methodology, CAS E- Forum Fall 2010, 43-104.
  • Bradu D., Mundlak Y. (1970). Estimation in Lognormal Lineer Models, JASA Vol. 6, 198-211.
  • Bühlmann H. (1983). Estimation of IBNR Reserves by The Methods of Chain- Ladder, Cape-Cod, and Complementary Loss Ratio, International Summer School 1983, Unpublished.
  • Dropkin L. B. (1964). Size of Loss Distributions in Workmen’s Compensation Insurance, Proc. CAS 51, 198-242.
  • England P. D., Verrall R. J. (2002). Standard Errors of Prediction in Claims Reserving: A Comparison of Methods, General Insurance Colloquium, Actuaries, Vol. 1, 459-478. & Institute of
  • Finney D. J. (1941). On the Distribution of a Variate Whose Logarithm is Normally Distributed, JRSS Suppl. 7, 155-161.
  • Friedland J. (2009). Estimating Unpaid Claims using Basic Techniques, CAS-FCAS, KPMG LLP, Version II.
  • Hewitt C. C. (1966). Distribution by Size of Risk-A Model, Proc. CAS 53, 106-115.
  • Jing Y., Lebens J., Lowe S. (2009). Claim Reserving: Performance Testing and The Control Cycle, CAS: Variance Advancing The Science of Risk, Vol. 3 Issue 2. Khury C. K. (1980). Loss Reserves: Performance Standards , Proc. CAS 67, 1- 21.
  • Klugman S. A., Panjer H. H., Willmot G. E. (2004). Loss Models: From Data to Decisions, Willey&Sons Ltd. Edition, John
  • Mack T. (1999). The Standard Error of Chain- Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor, ASTIN Bulletin 29, 361-366.
  • Narayan P., Warthen, T. V. (2000). A Comparative Study of The Performance of Loss Reserving Methods Through Simulation: Journal of Actuarial Practice, Vol. 8. Patrik G. (1980). Estimating Casualty
  • Insurance Loss Amount Distributions,
  • Proc. CAS 67, 57-109.
  • Pentikäinen T., Rantala J. (1992). A Simulation Procedure Claims Reserving Methods, ASTIN Bull, Vol. 22, No. 2, 191-216. Different
  • Renshaw A. E., Verrall R. J. (1998). A Stochastic Model Underlying The Chain- Ladder Technique, British Actuarial Journal, Vol. 4, 903-923.
  • Rollins J. W. (1997). Performance Testing Aggregate and Structural Reserving Methods: A Simulation Approach, CAS Forum Summer 1997, Vol. 1, 137-173.
  • Schmidt K. D., Zocher M. (2008). The Bornhuetter-Ferguson Principle, CAS: Variance Advancing The Science of Risk, Vol. 3 Issue 2.
  • Stanard J. N. (1985). A Simulation Test of Prediction Errors of Loss Reserving Techniques, CAS Proceedings May 1985, Vol. 72, 124-148.
  • Verrall R. J. (1991). On The Unbiased Estimation of Reserves from Loglinear Models, Insurance: Mathematics and Economics, 10, 1, 75-80.
  • Verrall R. J. (1994). Statistical Methods for The Chain Ladder Technique, CAS Forum Spring 1994, 393-446.
  • Wiser R. F. (2001). Loss Reserving, Revised and Updated By Jo Ellen Cockley and Andrea Gardner, In: Foundations of Casualty Actuarial Science, New York, 197-285
  • Wüthrich M. V, Merz M. (2008). Stochastic Claims Reserving Methods in Insurance, John Willey&Sons Ltd.  
There are 24 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Ezgi Nevruz

Yasemin Gençtürk This is me

Publication Date May 5, 2015
Published in Issue Year 2014 Volume: 15 Issue: 1

Cite

APA Nevruz, E., & Gençtürk, Y. (2015). BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 15(1), 15-31. https://doi.org/10.18038/btd-a.74130
AMA Nevruz E, Gençtürk Y. BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI. AUJST-A. May 2015;15(1):15-31. doi:10.18038/btd-a.74130
Chicago Nevruz, Ezgi, and Yasemin Gençtürk. “BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 15, no. 1 (May 2015): 15-31. https://doi.org/10.18038/btd-a.74130.
EndNote Nevruz E, Gençtürk Y (May 1, 2015) BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 15 1 15–31.
IEEE E. Nevruz and Y. Gençtürk, “BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI”, AUJST-A, vol. 15, no. 1, pp. 15–31, 2015, doi: 10.18038/btd-a.74130.
ISNAD Nevruz, Ezgi - Gençtürk, Yasemin. “BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 15/1 (May 2015), 15-31. https://doi.org/10.18038/btd-a.74130.
JAMA Nevruz E, Gençtürk Y. BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI. AUJST-A. 2015;15:15–31.
MLA Nevruz, Ezgi and Yasemin Gençtürk. “BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 15, no. 1, 2015, pp. 15-31, doi:10.18038/btd-a.74130.
Vancouver Nevruz E, Gençtürk Y. BAZI HASAR REZERV YÖNTEMLERİNİN PERFORMANSININ BENZETİM İLE KARŞILAŞTIRILMASI. AUJST-A. 2015;15(1):15-31.