Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T14:29:07.963Z Has data issue: false hasContentIssue false
  • English
  • Français

Cash Flow Simulation for a Model of Outstanding Liabilities Based on Claim Amounts and Claim Numbers

Published online by Cambridge University Press:  09 August 2013

María Dolores Martínez Miranda ,
Bent Nielsen ,
Jens Perch Nielsen  and
Richard Verrall
María Dolores Martínez Miranda
Affiliation:
University of Granada, Campus Fuentenueva, 18071, Granada, Spain, E-mail: [email protected]
Bent Nielsen
Affiliation:
Nuffield College, Oxford OX1 1NF, U.K., E-mail: [email protected]
Jens Perch Nielsen
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, U.K., E-mail: [email protected]
Richard Verrall
Affiliation:
Cass Business School, City University London, E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we develop a full stochastic cash flow model of outstanding liabilities for the model developed in Verrall, Nielsen and Jessen (2010). This model is based on the simple triangular data available in most non-life insurance companies. By using more data, it is expected that the method will have less volatility than the celebrated chain ladder method. Eventually, our method will lead to lower solvency requirements for those insurance companies that decide to collect counts data and replace their conventional chain ladder method.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 1 , May 2011 , pp. 107 - 129
Copyright
Copyright © International Actuarial Association 2011

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 306–331.Google Scholar
Björkwall, S., Hössjer, O. and Ohlsson, E. (2009b) Bootstrapping the separation method in claims reserving. Stockholm University, Mathematical Statistics, Research Report 2009:2. To appear in ASTIN Bulletin.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.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
Gesmann, M. (2009) R-package ‘ChainLadder’ version 0.1.2-11 (April, 17, 2009).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.Google 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.Google Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2010) Forecasting in an extended chain-ladder-type model. Journal of Risk and Insurance, to appear.Google Scholar
Mack, T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 21, 93–109.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 70, 701–714.Google Scholar
R Development Core Team (2006) R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.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.Google Scholar
Verrall, R., Nielsen, J.P. and Jessen, A. (2010) Prediction of RBNS and IBNR claims using claim amounts and claim counts. To appear in ASTIN Bulletin.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