×

Double chain ladder and Bornhuetter-Ferguson. (English) Zbl 1515.91137

Summary: In this article we propose a method close to double chain ladder (DCL) introduced by D. M. Martínez Miranda et al. [ASTIN Bull. 42, No. 1, 59–76 (2012; Zbl 1277.91092)]. The proposed method is motivated by the potential lack of stability of the DCL method (and of the classical chain ladder method [CLM] itself). We consider the implicit estimation of the underwriting year inflation in the CLM method and the explicit estimation of it in DCL. This may represent a weak point for DCL and CLM because the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. We include an empirical illustration that illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method. We also apply bootstrap estimation to approximate the predictive distributions.

MSC:

91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics
62F40 Bootstrap, jackknife and other resampling methods

Citations:

Zbl 1277.91092

Software:

R; DCL
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Alai, D. H.; Merz, M.; Wüthrich, M. V., Mean Square Error of Prediction in the Bornhuetter-Ferguson Claims Reserving Method, Annals of Actuarial Science, 4, 1, 7-31 (2009)
[2] Alai, D. H.; Merz, M.; Wüthrich, M. V., Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited, Annals of Actuarial Science, 5, 1, 7-17 (2010)
[3] Bornhuetter, R. L.; Ferguson, R. E., The Actuary and IBNR, Proceedings of the Casualty Actuarial Society, 59, 181-195 (1972)
[4] England, P.; Verrall, R., Analytic and Bootstrap Estimates of Prediction Error in Claims Reserving, Insurance: Mathematics and Economics, 25, 281-293 (1999) · Zbl 0944.62093
[5] Kuang, D.; Nielsen, B.; Nielsen, J. P., Chain-Ladder as Maximum Likelihood Revisited, Annals of Actuarial Science, 4, 1, 105-121 (2009)
[6] Mack, T., A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves, ASTIN Bulletin, 39, 35-60 (1991)
[7] Mack, T., The Prediction Error of Bornhuetter/Ferguson, ASTIN Bulletin, 38, 1, 87-103 (2008) · Zbl 1169.91426
[8] Martínez-Miranda, M. D.; Nielsen, B.; Nielsen, J. P.; Verrall, R., Cash Flow Simulation for a Model of Outstanding Liabilities Based on Claim Amounts and Claim Numbers, ASTIN Bulletin, 41, 1, 107-129 (2011)
[9] Martínez-Miranda, M. D.; Nielsen, J. P.; Verrall, R., Double Chain Ladder, ASTIN Bulletin, 42, 1, 59-76 (2012) · Zbl 1277.91092
[10] Martínez-Miranda, M. D.; Nielsen, J. P.; Wüthrich, M. V., Statistical Modelling and Forecasting in Non-life Insurance, SORT—Statistics and Operations Research Transactions, 36, 2, 195-218 (2012) · Zbl 1296.62209
[11] R Development Core Team, R: A Language and Environment for Statistical Computing (2006), Vienna: R Foundation for Statistical Computing, Vienna
[12] Schmidt, K. D.; Zocher, M., The Bornhuetter-Ferguson Principle, Variance: Advancing the Science of Risk, 2, 1, 85-110 (2008)
[13] Verrall, R., Chain Ladder and Maximum Likelihood, Journal of the Institute of Actuaries, 118, 489-499 (1991)
[14] Verrall, R., Stochastic Models for the Bornhuetter-Ferguson Technique, North American Actuarial Journal, 8, 3, 67-89 (2004) · Zbl 1085.62516
[15] Verrall, R.; Nielsen, J. P.; Jessen, A., Prediction of RBNS and IBNR Claims Using Claim Amounts and Claim Counts, ASTIN Bulletin, 40, 2, 871-887 (2010) · Zbl 1235.91109
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.