Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Prediction in run-off triangle using Bayesian linear model

삼각분할표 자료에서 베이지안 모형을 이용한 예측

  • Lee, Ju-Mi (Clinical Trial Center, Kyungpook National University Hospital) ;
  • Lim, Jo-Han (Department of Statistics, Seoul National University) ;
  • Hahn, Kyu-S. (Underwood International College, Yonsei University) ;
  • Lee, Kyeong-Eun (Department of Statistics, Kyungpook National University)
  • 이주미 (경북대학교 병원 임상시험센터) ;
  • 임요한 (서울대학교 통계학과) ;
  • 한규섭 (연세대학교 언더우드 국제학부) ;
  • 이경은 (경북대학교 통계학과)
  • Published : 2009.03.31
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Abstract

In the current paper, by extending Verall (1990)'s work, we propose a new Bayesian model for analyzing run-off triangle data. While Verall's (1990) work only account for the calendar year and evolvement time effects, our model further accounts for the "absolute time" effects. We also suggest a Markov Chain Monte Carlo method that can be used for estimating the proposed model. We apply our proposed method to analyzing three empirical examples. The results demonstrate that our method significantly reduces prediction error when compared with the existing methods.

본 논문은 삼각 분할표 자료의 예측문제에 있어 Verrall (1990)의 발생연도효과와 경과년도효과만 있는 베이지안 선형모형을 절대연도효과가 있는 모형으로 확장한 모형을 제시하고 이에 대한 추정 방법으로 마르코프 연쇄 몬테칼로 방법을 제안한다. 제안된 모형과 추정 방법은 세 가지 실제 예를 통하여 기존의 방법들에 비해서 일반적으로 작은 상대 예측오차를 제공함을 보였다.

Keywords

References

  1. 황형태, 이성임, 방미진 (2005). 이혼율에 대한 새로운 지표의 개발 및 적용 : 1990-2003년도의 우리나라 이혼률 분석. <통계연구>, 10, 23-37.
  2. Barnett, G. and Zehnwirth, B. (2000). Best estimates for reserves. Proceedings of the Casualty Actuarial Society , LXXXVII, 245-303.
  3. Brosius, E. (1992). Loss development using credibility. Casualty Actuarial Society Part 7 Exam Study Kit.
  4. De Vylder, F. and Goovaerts, M. J. (1979). Proceedings of the first meeting of the contact group "Actuarial Science", KU Leuven, Belgium.
  5. England, P. D and Verrall, R. J. (2002). Stochastic claims reserving in general insurance (with discussion). British Actuarial Journal, 8, III.
  6. Kim, Y. (2006). A Comparative study for several bayesian estimators under balanced loss function. Journal of the Korean Data & Information Science Society, 17, 291-300.
  7. Kremer, E. (1982). IBNR-Claims and the two-way model of ANOVA. Scandinavian Actuarial Journal, 1, 47-55.
  8. Lee, S. (2007). Population projections for local governments in Korea: based on Hamilton-Perry & Auto regression. Journal of the Korean Data & Information Science Society, 18, 955-961.
  9. 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
  10. Mack, T. (1994). Which stochastic model is underlying the chain ladder method?. Insurance: Mathematics and Economics, 15, 133-138. https://doi.org/10.1016/0167-6687(94)90789-7
  11. Murphy (1994). Unbiased loss development factors. Proceedings of the Casualty Actuarial Society, LXXXI, 154-222.
  12. Verrall, R. J. (1990). Bayes and empirical bayes estimation for the chain ladder model. Astin Bulletin, 20, 217-243. https://doi.org/10.2143/AST.20.2.2005444
  13. Zehnwirth, B. (1994). Probabilistic development factor models with applications to loss reserve variability, prediction intervals and risk based capital. Casualty Actuarial Society Forum, Spring 1994, 2.