Skip to main content Accessibility help

Bootstrapping Individual Claim Histories

  • Stig Rosenlund (a1)


The bootstrap method BICH is given for estimating mean square prediction errors and predictive distributions of non-life claim reserves under weak conditions. The dates of claim occurrence, reporting and finalization and the payment dates and amounts of individual finalized historic claims form a claim set from which samples with replacement are drawn. We assume that all claims are independent and that the historic claims are distributed as the object claims, possibly after inflation adjustment and segmentation on a background variable, whose distribution could have changed over time due to portfolio change. Also we introduce the new reserving function RDC, using all these dates and payments for reserve predictions. We study three reserving functions: chain ladder, the Schnieper (1991) method and RDC. Checks with simulated cases obeying the assumptions of Mack (1999) for chain ladder and Liu and Verrall (2009) for Schnieper's method, respectively, confirm the validity of our method. BICH is used to compare the three reserving functions, of which RDC is found overall best in simulated cases.



Hide All
Björkwall, S., Hössjer, O. and Ohlsson, E. (2009) Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving. Scandinavian Actuarial Journal, 2009(4), 306331.
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8(iii), 443518.
Fisher, W.H. and Lange, J.T. (1973) Loss reserve testing: a report year approach. Proceedings of the Casualty Actuarial Society, 60, 189207.
Hachemeister, C.A. and Stanard, J.N. (1975) IBNR claims count estimation with static lag functions. Spring meeting of the Casualty Actuarial Society.
Kuang, D., Nielsen, B. and Nielsen, J.P. (2009) Chain-ladder as maximum likelihood revisited. Annals of Actuarial Science, 4(1), 105121.
Larsen, C.R. (2007) An individual claims reserving model. ASTIN Bulletin, 37(1), 113132.
Liu, H. and Verrall, R.J. (2009) Predictive distributions for reserves which separate true IBNR and IBNER claims. ASTIN Bulletin, 39(1), 3560.
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213225.
Mack, T. (1999) The standard error of chain ladder reserve estimates: recursive calculation and inclusion of a tail factor. ASTIN Bulletin, 29(2), 361366.
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23(1), 95115.
Norberg, R. (1999) Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin, 29(1), 525.
Sawkins, R.W. (1979) Methods of analysing claim payments in general insurance. Transactions of the Institute of Actuaries of Australia, 435519.
Schnieper, R. (1991) Separating true IBNR and IBNER claims. ASTIN Bulletin, 21(1), 111127.
Taylor, G., McGuire, G. and Sullivan, J. (2008) Individual claim loss reserving conditioned by case estimates. Annals of Actuarial Science, 3, 215256.
Taylor, G. (2011) Maximum likelihood and estimation efficiency of the chain ladder. ASTIN Bulletin, 41(1), 131155.
Verrall, R., Nielsen, J.P. and Jessen, A. (2010) Prediction of RBNS and IBNR claims using claim amounts and claim counts. ASTIN Bulletin, 40(1), 871887.
Wilcox, R. (1997) Introduction to Robust Estimation and Hypothesis Testing. Academic Press.
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.
Zhao, X. and Zhou, X. (2010) Applying copula models to individual claim loss reserving methods. Insurance: Mathematics and Economics, 46(2), 290299.


Bootstrapping Individual Claim Histories

  • Stig Rosenlund (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed