Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T15:21:55.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Bootstrapping Individual Claim Histories

Published online by Cambridge University Press:  09 August 2013

Stig Rosenlund
Stig Rosenlund*
Affiliation:
Länsförsäkringar Alliance, Sweden (retired), Stockholm, Sweden, E-mail: stig.rosenlund@sverige.nu
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

BICHBootstrapClaim reserveRDCStochastic reserving
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 291 - 324
Copyright
Copyright © International Actuarial Association 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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), 306–331.CrossRefGoogle Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8(iii), 443–518.CrossRefGoogle Scholar
Fisher, W.H. and Lange, J.T. (1973) Loss reserve testing: a report year approach. Proceedings of the Casualty Actuarial Society, 60, 189–207.Google Scholar
Hachemeister, C.A. and Stanard, J.N. (1975) IBNR claims count estimation with static lag functions. Spring meeting of the Casualty Actuarial Society.Google Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2009) Chain-ladder as maximum likelihood revisited. Annals of Actuarial Science, 4(1), 105–121.CrossRefGoogle Scholar
Larsen, C.R. (2007) An individual claims reserving model. ASTIN Bulletin, 37(1), 113–132.CrossRefGoogle Scholar
Liu, H. and Verrall, R.J. (2009) Predictive distributions for reserves which separate true IBNR and IBNER claims. ASTIN Bulletin, 39(1), 35–60.CrossRefGoogle Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.CrossRefGoogle Scholar
Mack, T. (1999) The standard error of chain ladder reserve estimates: recursive calculation and inclusion of a tail factor. ASTIN Bulletin, 29(2), 361–366.CrossRefGoogle Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23(1), 95–115.CrossRefGoogle Scholar
Norberg, R. (1999) Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin, 29(1), 5–25.CrossRefGoogle Scholar
Sawkins, R.W. (1979) Methods of analysing claim payments in general insurance. Transactions of the Institute of Actuaries of Australia, 435–519.Google Scholar
Schnieper, R. (1991) Separating true IBNR and IBNER claims. ASTIN Bulletin, 21(1), 111–127.CrossRefGoogle Scholar
Taylor, G., McGuire, G. and Sullivan, J. (2008) Individual claim loss reserving conditioned by case estimates. Annals of Actuarial Science, 3, 215–256.CrossRefGoogle Scholar
Taylor, G. (2011) Maximum likelihood and estimation efficiency of the chain ladder. ASTIN Bulletin, 41(1), 131–155.Google Scholar
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), 871–887.Google Scholar
Wilcox, R. (1997) Introduction to Robust Estimation and Hypothesis Testing. Academic Press.Google Scholar
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.Google Scholar
Zhao, X. and Zhou, X. (2010) Applying copula models to individual claim loss reserving methods. Insurance: Mathematics and Economics, 46(2), 290–299.Google Scholar