Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T14:52:53.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling the Claim Duration of Income Protection Insurance Policyholders using Parametric Mixture Models

Published online by Cambridge University Press:  10 May 2011

D. G. W. Pitt
D. G. W. Pitt
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Parkville 3502, Victoria, Australia., Email: dgpitt@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the modelling of claim durations for existing claimants under income protection insurance policies. A claim is considered to be terminated when the claimant returns to work. Data used in the analysis were provided by the Life and Risk Committee of the Institute of Actuaries of Australia. Initial analysis of the data suggests the presence of a long-run probability, of the order of 7%, that a claimant will never return to work. This phenomenon suggests the use of mixed parametric regression models as a description of claim duration which include the prediction of a long-run probability of not returning to work. A series of such parametric mixture models was investigated, and it was found that the generalised F mixture distribution provided a good fit to the data and also highlighted the impact of a number of statistically significant predictors of claim duration.

Keywords

Income Protection InsuranceMixture ModelsClaim Termination RatesMaximum Likelihood
Type
Papers
Information
Annals of Actuarial Science , Volume 2 , Issue 1 , March 2007 , pp. 1 - 24
Copyright
Copyright © Institute and Faculty of Actuaries 2007

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

Andersen, P.K. & Gill, R.D. (1982). Cox's regression model counting process: a large sample study. Annals of Statistics, 10, 1100–1120.CrossRefGoogle Scholar
Arjas, E. (1988). A graphical method for assessing goodness of fit in Cox's proportional hazards model. Journal of the American Statistical Association, 83, 204–212.CrossRefGoogle Scholar
CMIB (1991). Continuous Mortality Investigation Report No 12. Institute and Faculty of Actuaries, U.K.Google Scholar
Cox, D. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, B, 34, 187–220.Google Scholar
Grambsch, P.M. & Therneau, T.M. (1994). Proportional hazard tests and diagnostics based on weighted residuals. Biometrika, 81, 515–526.CrossRefGoogle Scholar
Gregorius, F.K. (1993). Disability insurance in the Netherlands. Insurance: Mathematics and Economics, 13, 101–116.Google Scholar
Harrell, F.E. (1986). The PHGLM procedure. SUGI Supplemental Library Guide, Version 5 edition, Cary, NC: SAS Institute Inc.Google Scholar
Kaplan, E.L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457–481.CrossRefGoogle Scholar
Maller, R. & Zhou, X. (1995). Survival analysis with long term survivors. Wiley, New York.Google Scholar
Peng, Y., Dear, K.B. & Denham, J.W. (1998). A generalized F mixture model for cure rate estimation. Statistics in Medicine, 17(8), 813–830.3.0.CO;2-#>CrossRefGoogle ScholarPubMed
Pitt, D. (2006). Actuarial models for the analysis of disability income insurance. University of Melbourne working paper series: http://www.economics.unimelb.edu.au/actwww/wps2006.htmlGoogle Scholar
Robinson, M.A. (1988). The 1985 CIDA disability table. Institute of Actuaries of Australia Quarterly Journal, December 1988.Google Scholar
Segerer, G. (1993). The actuarial treatment of disability risk in Germany, Austria and Switzerland. Insurance: Mathematics and Economics, 13, 131–140.Google Scholar
The Institute of Actuaries of Australia (1997). Report of the Disability Committee. Transactions of the Institute of Actuaries of Australia, 489–576.Google Scholar
Therneau, T.M. & Grambsch, P.M. (2000). Modeling survival data: extending the Cox model. Springer, New York.CrossRefGoogle Scholar