Communications for Statistical Applications and Methods

  • 제24권3호
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  • Pages.211-226
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  • 2017
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Consideration of a structural-change point in the chain-ladder method

  • Kwon, Hyuk Sung (Department of Statistics and Actuarial Science, Soongsil University) ;
  • Vu, Uy Quoc (Department of Statistics and Actuarial Science, Soongsil University)
  • 투고 : 2016.11.16
  • 심사 : 2017.03.18
  • 발행 : 2017.05.31
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초록

The chain-ladder method, for which run-off data is employed is popularly used in the rate-adjustment and loss-reserving practices of non-life-insurance and health-insurance companies. The method is applicable when the underlying assumption of a consistent development pattern is in regards to a cumulative loss payment after the occurrence of an insurance event. In this study, a modified chain-ladder algorithm is proposed for when the assumption is considered to be only partially appropriate for the given run-off data. The concept of a structural-change point in the run-off data and its reflection in the estimation of unpaid loss amounts are discussed with numerical illustrations. Experience data from private health insurance coverage in Korea were analyzed based on the suggested method. The performance in estimation of loss reserve was also compared with traditional approaches. We present evidence in this paper that shows that a reflection of a structural-change point in the chain-ladder method can improve the risk management of the relevant insurance products. The suggested method is expected to be utilized easily in actuarial practice as the algorithm is straightforward.

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참고문헌

  1. Bornhuetter RL and Ferguson RE (1972). The actuary and IBNR, Proceedings of the Casualty Actuarial Society, 59, 181-195.
  2. Brown RL and Lennox WS (2015). Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance (4th ed), ACTEX Publications, Winsted.
  3. Casualty Actuarial Society (2001). Foundations of Casualty Actuarial Science (4th ed), Casualty Actuarial Society, New York.
  4. England PD, Verrall RJ, and Wuthrich MV (2012). Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method, Annals of Actuarial Science, 6, 258-283. https://doi.org/10.1017/S1748499512000012
  5. Heberle J and Thomas A (2014). Combining chain-ladder claims reserving with fuzzy numbers, Insurance: Mathematics and Economics, 55, 96-104. https://doi.org/10.1016/j.insmatheco.2014.01.002
  6. Hess KT and Schmidt KD (2002). A comparison of models for the chain-ladder method, Insurance: Mathematics and Economics, 31, 351-364. https://doi.org/10.1016/S0167-6687(02)00160-9
  7. Kremer E (1982). IBNR-claims and the two-way model of ANOVA, Scandinavian Actuarial Journal, 1982, 47-55. https://doi.org/10.1080/03461238.1982.10405432
  8. Lee I, Lee HS, and Kim HT (2014). Analysis of reserves in multiple life insurance using copula, Communications for Statistical Applications and Methods, 21, 23-43. https://doi.org/10.5351/CSAM.2014.21.1.023
  9. Lee SI (2008). Testing structural changes in triangular data, Communications of the Korean Statistical Society, 15, 551-562.
  10. Mack T (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates, Astin Bulletin, 23, 213-225. https://doi.org/10.2143/AST.23.2.2005092
  11. Mack T and Venter G (2000). A comparison of stochastic models that reproduce chain ladder reserve estimates, Insurance: Mathematics and Economics, 26, 101-107. https://doi.org/10.1016/S0167-6687(99)00039-6
  12. Martinez Miranda MD, Nielsen JP, Verrall R, and Wuthrich MV (2015). Double chain ladder, claims development inflation and zero-claims, Scandinavian Actuarial Journal, 2015, 383-405. https://doi.org/10.1080/03461238.2013.823459
  13. Pesta M and Hudecova S (2012). Asymptotic consistency and inconsistency of the chain ladder, Insurance: Mathematics and Economics, 51, 472-479. https://doi.org/10.1016/j.insmatheco.2012.07.004
  14. Peters GW, Wuthrich MV, Shevchenko PV (2010). Chain ladder method: Bayesian bootstrap versus classical bootstrap, Insurance: Mathematics and Economics, 47, 36-51. https://doi.org/10.1016/j.insmatheco.2010.03.007
  15. Renshaw AE and Verrall RJ (1998). A stochastic model underlying the chain-ladder technique, British Actuarial Journal, 4, 903-923. https://doi.org/10.1017/S1357321700000222
  16. Riegel U (2014). A bifurcation approach for attritional and large losses in chain ladder calculations, Astin Bulletin, 44, 127-172. https://doi.org/10.1017/asb.2013.27
  17. Schiegl M (2015). A model study about the applicability of the chain-ladder method, Scandinavian Actuarial Journal, 6, 482-499.
  18. Schmidt KD (1997). Non-optimal prediction by the chain ladder method, Insurance: Mathematics and Economics, 21, 17-24. https://doi.org/10.1016/S0167-6687(97)00015-2
  19. Tarbell TF (1934). Incurred but not reported claim reserves. In Proceedings of the Casualty Actuarial Society, 20, 275-280.
  20. Taylor G (2011). Maximum likelihood and estimation efficiency of the chain ladder, Astin Bulletin, 41, 131-155.
  21. Taylor G (2015). Bayesian chain ladder models, Astin Bulletin, 45, 75-99. https://doi.org/10.1017/asb.2014.25
  22. Verdonck T and Van Wouwe M (2011). Detection and correction of outliers in the bivariate chain-ladder method, Insurance: Mathematics and Economics, 49, 188-193. https://doi.org/10.1016/j.insmatheco.2011.04.003
  23. Verrall RJ (2000). An investigation into stochastic claims reserving models and the chain-ladder technique, Insurance: Mathematics and Economics, 26, 91-99. https://doi.org/10.1016/S0167-6687(99)00038-4
  24. Verrall RJ and Wuthrich MV (2015). Parameter reduction in log-normal chain-ladder models, European Actuarial Journal, 5, 355-380. https://doi.org/10.1007/s13385-015-0114-7
  25. Wuthrich MV (2008). Prediction error in the chain ladder method, Insurance: Mathematics and Economics, 42, 378-388. https://doi.org/10.1016/j.insmatheco.2007.05.002
  26. Wuthrich MV and Merz M (2008). Stochastic Claims Reserving Methods in Insurance, John Wiley & Sons, West Sussex.