Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-11T05:14:05.261Z Has data issue: false hasContentIssue false

Negative incremental claims: chain ladder and linear models

Published online by Cambridge University Press:  20 April 2012

R. J. Verrall
Affiliation:
The City University, London
Z. Li
Affiliation:
The City University, London

Abstract

This paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1993

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

Ajne, B. (1989). Exponential Runoff. Claims Reserving Manual, 2. Institute of Actuaries.Google Scholar
Christofides, S. (1990). Regression models based on log-incremental claims. Claims Reserving Manual, 2. Institute of Actuaries.Google Scholar
Kremer, E. (1982). IBNR-Claims and the Two-way Model of ANOVA. Scand. Act. J. 1, 4755.CrossRefGoogle Scholar
Lt, Z. (1990). Maximum Likelihood Methods in the Estimation of Outstanding Claims. M.Sc. Dissertation, Department of Actuarial Science and Statistics, City University.Google Scholar
Renshaw, A. E. (1989). Chain Ladder and Interactive Modelling. J.I.A. 116, 559587.Google Scholar
Verrall, R. J. (1990). Statistical Aspects of Outstanding Claims Reserving. Presented to a joint meeting of the Royal Statistical Society, General Applications Section, and the Staple Inn Actuarial Society.Google Scholar
Verrall, R. J. (1991a). Chain Ladder and Maximum Likelihood. J.I.A. 118, 489499.Google Scholar
Verrall, R. J. (1991b). On the Unbiased Estimation of Reserves from Loglinear Models. Insurance; Mathematics and Economics, 10, 7580.CrossRefGoogle Scholar
Zehnwirth, B. (1985). Interactive Claims Reserving Forecasting System. Benhar Nominees Pty Ltd, Tunuwurra, NSW, Australia.Google Scholar