Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T20:25:16.864Z Has data issue: false hasContentIssue false
  • English
  • Français

A Bootstrap Estimate of the Predictive Distribution of Outstanding Claims for the Schnieper Model

Published online by Cambridge University Press:  09 August 2013

Huijuan Liu  and
Richard Verrall
Huijuan Liu
Affiliation:
RBS Insurance, Churchill Court, 6th Floor, MP3, Bromley, BD1 1DP., E-Mail: [email protected]
Richard Verrall
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ., E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the bootstrapping approach for measuring reserve uncertainty when applying the model of Schnieper for reserves which separate Incurred But Not Reported (IBNR) and Incurred But Not Enough Reserved (IBNER) claims. The Schnieper method has been explored in Liu and Verrall (2009), and the Mean Square Errors of Prediction (MSEP) derived. This paper takes this further by deriving the full predictive distribution, using bootstrapping. Numerical examples are provided and the MSEP from the bootstrapping approach are compared with those obtained analytically.

Keywords

BootstrappingClaims ReservingSchnieper modelIBNR and IBNER claims
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 677 - 689
Copyright
Copyright © International Actuarial Association 2009

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

Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M.V. (2006) The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy revisited). ASTIN Bulletin, 36, 522–542.Google Scholar
England, P.D. (2002) Addendum to “Analytic and bootstrap estimates of prediction errors in claims reserving”. Insurance: Mathematics and Economics, 31, 461–466.Google Scholar
England, P.D. and Verrall, R.J. (1999) Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25, 281–293.Google Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic Claims Reserving in General Insurance (with discussion). British Actuarial Journal, 8, 443–544.Google Scholar
England, P.D. and Verrall, R.J. (2006) Predictive Distributions of Outstanding Liabilities in General Insurance. Annals of Actuarial Science, 1, 221–270.Google Scholar
Liu, H. and Verrall, R. (2009) Predictive Distributions for Reserves which Separate True IBNR and IBNER Claims. ASTIN Bulletin, 39, 35–60.Google Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23, 214–225.Google Scholar
Peters, G., Wüthrich, M. and Shevchenko, P. (2009) Chain Ladder Method: Bayesian Bootstrap versus Classical Bootstrap. Research Report, ETH Zurich.Google Scholar
Schnieper, R. (1991) Separating True IBNR and IBNER Claims. ASTIN Bulletin, 21, 111–127.Google Scholar