Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T08:14:02.524Z Has data issue: false hasContentIssue false
  • English
  • Français

Double Chain Ladder

Published online by Cambridge University Press:  09 August 2013

María Dolores Martínez Miranda ,
Jens Perch Nielsen  and
Richard Verrall
María Dolores Martínez Miranda
Affiliation:
University of Granada, Spain, E-mail: mmiranda@ugr.es
Jens Perch Nielsen
Affiliation:
Cass Business School, City University London, U.K., E-mail: Jens.Nielsen.1@city.ac.uk
Richard Verrall
Affiliation:
Cass Business School, City University London, U.K., E-mail: R.J.Verrall@city.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

By adding the information of reported count data to a classical triangle of reserving data, we derive a suprisingly simple method for forecasting IBNR and RBNS claims. A simple relationship between development factors allows to involve and then estimate the reporting and payment delay. Bootstrap methods provide prediction errors and make possible the inference about IBNR and RBNS claims, separately.

Keywords

BootstrappingChain LadderClaims ReservesReserve Risk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 59 - 76
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. (2009a) Non-parametric and Parametric Bootstrap Techniques for Arbitrary Age-to-Age Development Factor Methods in Stochastic Claims Reserving. Scandinavian Actuarial Journal, 4, 306–331.CrossRefGoogle Scholar
Björkwall, S., Hössjer, O. and Ohlsson, E. (2009b) Bootstrapping the separation method in claims reserving. ASTIN Bulletin 40(2), 845–869.Google Scholar
Bryden, D. and Verrall, R.J. (2009) Calendar year effects, claims inflaton and the Chain-Ladder technique. Annals of Actuarial Science 4, 287–301.CrossRefGoogle Scholar
Bühlmann, H., Schnieper, R. and Straub, E. (1980) Claims reserves in casualty insurance based on a probability model. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker.Google Scholar
England, P. (2002) Addendum to “Analytic and Bootstrap Estimates of Prediction Error in Claims Reserving”. Insurance: Mathematics and Economics 31, 461–466.Google Scholar
England, P. and Verrall, R. (1999) Analytic and Bootstrap Estimates of Prediction Error 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.CrossRefGoogle Scholar
England, P. and Verrall, R. (2006) Predictive Distributions of Outstanding Liabilities in General Insurance. Annals of Actuarial Science, 1(2), 221–270.Google Scholar
Gesmann, M., Wayne, Z. and Murphy, D. (2011) R-package “ChainLadder” version 0.1.4-3.4 (22 March, 2011). URL: http://code.google.com/p/chainladder/ Google Scholar
Kremer, E. (1985) Einführung in die Versicherungsmathematik. Göttingen: Vandenhoek & Ruprecht.Google Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2008a) Identification of the age-period-cohort model and the extended chain-ladder model. Biometrika 95, 979–986.CrossRefGoogle Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2008b) Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika 95, 987–991.Google Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2009) Chain Ladder as Maximum Likelihood Revisited. Annals of Actuarial Science 4, 105–121.CrossRefGoogle Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2011) Forecasting in an extended chain-ladder-type model. Journal of Risk and Insurance 78, 345–359.Google Scholar
Mack, T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 39, 35–60.Google Scholar
Martínez-Miranda, M.D., Nielsen, B., Nielsen, J.P. and Verrall, R. (2011) Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers. ASTIN Bulletin, 41(1), 107–129.Google Scholar
Norberg, R. (1986) A contribution to modelling of IBNR claims. Scandinavian Actuarial Journal, 3, 155–203.Google 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 claims: Model variations and extensions. Astin Bulletin, 29(1), 5–25.Google Scholar
Pinheiro, P.J.R., Andrade e Silva, J.M. and Centeno, M.d.L. (2003) Bootstrap Methodology in Claim Reserving. Journal of Risk and Insurance 4, 701–714.CrossRefGoogle Scholar
R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (Austria). URL: http://www.R-project.org Google Scholar
Renshaw, A.E. and Verrall, R. (1998) A stochastic model underlying the chain ladder technique. British Actuarial Journal, 4, 903–923.Google Scholar
Taylor, G. (1977) Separation of inflation and other effects from the distribution of non-life insurance claim delays. ASTIN Bulletin 9, 217–230.CrossRefGoogle Scholar
Verrall, R. (1991) Chain ladder and Maximum Likelihood. Journal of the Institute of Actuaries 118, 489–499.Google Scholar
Verrall, R. (2000) An Investigation into Stochastic Claims Reserving Models and the Chain-Ladder Technique. Insurance: Mathematics and Economics 26, 91–99.Google Scholar
Verrall, R., Nielsen, J.P. and Jessen, A. (2010) Including Count Data in Claims Reserving. ASTIN Bulletin 40(2), 871–887.Google Scholar
Wüthrich, M. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.Google Scholar
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, 447–605.Google Scholar