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Comparing the Performance of Stochastic Loss Reserving Methods for Different Loss Severity Distributions

Year 2017, Volume: 10 Issue: 2, 86 - 95, 30.12.2017

Abstract

In this paper, stochastic loss reserving methods are compared using the mean absolute percentage error criterion. For this purpose, loss development squares (upper-left development triangles and lower-right goal triangles) are simulated using individual losses with changing severity under the scenarios where various distributional assumptions are made. In this loss square generating method, the distribution and the development process of a loss are considered from its occurrence to the closure based on the reporting and settlement delays. After simulating the loss development squares, loss reserves are estimated with the inflation-adjusted chain-ladder method and three different logarithmic regression models. The performance of the loss reserving methods is examined by comparing the estimated and actual loss reserves for different distributions commonly used for individual loss amount modeling in non-life insurance. It is seen that logarithmic regression models generally perform better than chain-ladder method for the specified scenarios.

References

  • [1] K. Antonio, R. Plat, 2014, Micro-Level Stochastic Loss Reserving For General Insurance, Scandinavian Actuarial Journal, 2014(7): 649-669.
  • [2] D. Bradu, Y. Mundlak, 1970, Estimation in Lognormal Linear Models, Journal of the American Statistical Association (JASA), 65(329): 198-211.
  • [3] H. Bühlmann, R. Schnieper, E. Straub, 1980, Claims Reserves in Casualty Insurance Based on a Probabilistic Model, Mitteilungen der Vereinigung Schweiz. Versicherungsmathematiker, 80(1): 21-45.
  • [4] S. T. B. Choy, J. S. K. Chan, U. E. Makov, 2007, Model Selection for Loss Reserves: The Growing Triangle Technique, Life&Pensions Magazine, 5: 35-40.
  • [5] J. Friedland, 2009, Estimating Unpaid Claims Using Basic Techniques, CAS-FCAS, KPMG LLP, Version II.
  • [6] Y. Jing, J. Lebens, S. Lowe, 2009, Claim Reserving: Performance Testing and the Control Cycle, CAS: Variance Advancing the Science of Risk, 3(2): 1-33.
  • [7] P. Narayan, T. V. Warthen, 2000, A Comparative Study of the Performance of Loss Reserving Methods Through Simulation, Journal of Actuarial Practice, 8: 63-88.
  • [8] E. Nevruz, Y. Gençtürk, 2014, Bazı Hasar Rezerv Yöntemlerinin Performansının Benzetim ile Karşılaştırılması, Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering, 15(1): 15-31.
  • [9] T. Pentikäinen, J. Rantala, 1992, A Simulation Procedure for Comparing Different Claims Reserving Methods, ASTIN Bull, 22(2): 191-216.
  • [10] A. E. Renshaw, R. J. Verrall, 1998, A Stochastic Model Underlying the Chain-Ladder Technique, British Actuarial Journal, 4(4): 903-923.
  • [11] A. Ricotta, G. P. Clemente, 2016, An Extension of Collective Risk Model for Stochastic Claim Reserving, Journal of Applied Finance and Banking, 6(5): 45-62.
  • [12] K. D. Schmidt, M. Zocher, 2008, The Bornhuetter-Ferguson Principle, CAS: Variance Advancing the Science of Risk, 3(2): 85-110.
  • [13] J. N. Stanard, 1985, A Simulation Test of Prediction Errors of Loss Reserving Techniques, CAS Proceedings May 1985, 72: 124-148.
  • [14] R. J. Verrall, 1991, On the Estimation of Reserves from Loglinear Models, Insurance: Mathematics and Economics, 10(1): 75-80.

Farklı Hasar Şiddeti Dağılımları için Stokastik Hasar Rezerv Yöntemlerinin Tahmin Performansı

Year 2017, Volume: 10 Issue: 2, 86 - 95, 30.12.2017

Abstract

Bu çalışmada, ortalama mutlak yüzde hata kriteri ile stokastik hasar rezerv yöntemleri karşılaştırılmıştır. Bu amaçla, değişen tutarlı bireysel hasarlar kullanılarak çeşitli dağılım varsayımları yapılan senaryolar altında hasar gelişim kareleri (sol-üst gelişim üçgenleri ve sağ-alt hedef üçgenler) benzetimle üretilmiştir. Bu hasar karesi üretme yönteminde, bir hasarın dağılımı ile bildirilme ve kapatılma gecikmelerine bağlı olarak bir hasarın meydana gelmesinden kapatılmasına kadar geçen süredeki gelişim süreci ele alınır. Hasar gelişim karelerinin benzetim ile üretilmesinden sonra, hasar rezervleri enflasyon-düzeltmeli zincir merviden yöntemi ve üç farklı logaritmik regresyon modeliyle tahmin edilmiştir. Rezerv yöntemlerinin performansı, hayat dışı sigortalarda bireysel hasar tutarlarının modellenmesinde sıklıkla kullanılan çeşitli dağılımlar için tahmini ve gerçek hasar rezervleri karşılaştırılarak incelenmiştir. Logaritmik regresyon modellerinin, belirlenen senaryolar için çoğunlukla zincir merdiven yönteminden daha iyi performans gösterdiği görülmüştür.

References

  • [1] K. Antonio, R. Plat, 2014, Micro-Level Stochastic Loss Reserving For General Insurance, Scandinavian Actuarial Journal, 2014(7): 649-669.
  • [2] D. Bradu, Y. Mundlak, 1970, Estimation in Lognormal Linear Models, Journal of the American Statistical Association (JASA), 65(329): 198-211.
  • [3] H. Bühlmann, R. Schnieper, E. Straub, 1980, Claims Reserves in Casualty Insurance Based on a Probabilistic Model, Mitteilungen der Vereinigung Schweiz. Versicherungsmathematiker, 80(1): 21-45.
  • [4] S. T. B. Choy, J. S. K. Chan, U. E. Makov, 2007, Model Selection for Loss Reserves: The Growing Triangle Technique, Life&Pensions Magazine, 5: 35-40.
  • [5] J. Friedland, 2009, Estimating Unpaid Claims Using Basic Techniques, CAS-FCAS, KPMG LLP, Version II.
  • [6] Y. Jing, J. Lebens, S. Lowe, 2009, Claim Reserving: Performance Testing and the Control Cycle, CAS: Variance Advancing the Science of Risk, 3(2): 1-33.
  • [7] P. Narayan, T. V. Warthen, 2000, A Comparative Study of the Performance of Loss Reserving Methods Through Simulation, Journal of Actuarial Practice, 8: 63-88.
  • [8] E. Nevruz, Y. Gençtürk, 2014, Bazı Hasar Rezerv Yöntemlerinin Performansının Benzetim ile Karşılaştırılması, Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering, 15(1): 15-31.
  • [9] T. Pentikäinen, J. Rantala, 1992, A Simulation Procedure for Comparing Different Claims Reserving Methods, ASTIN Bull, 22(2): 191-216.
  • [10] A. E. Renshaw, R. J. Verrall, 1998, A Stochastic Model Underlying the Chain-Ladder Technique, British Actuarial Journal, 4(4): 903-923.
  • [11] A. Ricotta, G. P. Clemente, 2016, An Extension of Collective Risk Model for Stochastic Claim Reserving, Journal of Applied Finance and Banking, 6(5): 45-62.
  • [12] K. D. Schmidt, M. Zocher, 2008, The Bornhuetter-Ferguson Principle, CAS: Variance Advancing the Science of Risk, 3(2): 85-110.
  • [13] J. N. Stanard, 1985, A Simulation Test of Prediction Errors of Loss Reserving Techniques, CAS Proceedings May 1985, 72: 124-148.
  • [14] R. J. Verrall, 1991, On the Estimation of Reserves from Loglinear Models, Insurance: Mathematics and Economics, 10(1): 75-80.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ezgi Nevruz 0000-0002-1756-7906

Yasemin Gençtürk This is me 0000-0002-8916-8509

Publication Date December 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 2

Cite

IEEE E. Nevruz and Y. Gençtürk, “Comparing the Performance of Stochastic Loss Reserving Methods for Different Loss Severity Distributions”, JSSA, vol. 10, no. 2, pp. 86–95, 2017.