Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-17T04:24:47.464Z Has data issue: false hasContentIssue false
  • English
  • Français

An Essay at Measuring the Variance of Estimates of Outstanding Claim Payments

Published online by Cambridge University Press:  29 August 2014

Frank Ashe
Frank Ashe*
Affiliation:
E. S. Knight & Co. Research Centre, Sydney
*
E. S. Knight & Co. Research Centre, 71 York Street, Sydney, N.S.W. 2000, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The variance of statistical estimates of outstanding claim payments for long-tailed general insurance portfolios is examined. The variance's three components are discussed. As there is no accepted technique for measuring this variance three methods are investigated empirically for its measurement—a parametric method, the jackknife method, and the bootstrap method. No method stands out as superior to the others and it is recommended that all three be evaluated and used to gauge the possible errors in the estimation of outstanding claims.

Type
Astin Competition 1985: Prize-Winning Papers and Other Selected Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue S1 , April 1986 , pp. S99 - S113
Copyright
Copyright © International Actuarial Association 1986

References

Baker, R. J. and Nelder, J. A. (1978) The GLIM System, Release 3: Generalized Linear Interactive Modelling. Numerical Algorithms Group: Oxford.Google Scholar
Bartholomew, D. J. (1975) Errors of Prediction in Markov Chain Models. Journal of the Royal Statistical Society B 37, 444–456.Google Scholar
De Jong, P. and Zehnwirth, B. (1980) A Random Coefficients Approach to Claims Reserving. Research Paper no. 219: School of Economic and Financial Studies, Macquarie University, North Ryde.Google Scholar
De Jong, P. and Zehnwirth, B. (1982) Claims Reserving, State-space models and the Kalman Filter, Journal of the Institute of Actuaries 110, 157–182.CrossRefGoogle Scholar
Freedman, D. A. and Peters, S. C. (1984) Bootstrapping a Regression Equation: Some Empirical Results. Journal of the American Statistical Association 79, 97–106.CrossRefGoogle Scholar
Martin-Lof, P. (1974) The Notion of Redundancy and Its Use as a Quantitative Measure of the Discrepancy between a Statistical Hypothesis and a Set of Observational Data. Scandinavian Journal of Statistics 1, 3–18.Google Scholar
Miller, A. J. (1984) Selection of Subsets of Regression Variables. Journal of the Royal Statistical Society A 147, 389–425.CrossRefGoogle Scholar
Miller, R. G. (1974) The Jackknife-A Review. Biometrika 61, 1–15.Google Scholar
Quenouille, M. H. (1974) Notes on Bias in Estimation. Biometrika 43, 353–360.CrossRefGoogle Scholar
Rey, W. J. J. (1979) Robust Statistical Methods. Lecture Notes in Mathematics v690, Springer-Verlag: Berlin.Google Scholar
Taylor, G. C. (1981) An Invariance Principle for the Analysis of Non–life Insurance Claims. Journal of the Institute of Actuaries 110, 205–242.CrossRefGoogle Scholar
Taylor, G. C. (1985) Combination of Estimates of Outstanding Claims in Non-Life Insurance. Insurance: Mathematics & Economics 4, 81–91.Google Scholar
Taylor, G. C. and Ashe, F. R. (1983) Second Moments of Estimates of Outstanding Claims. Journal of Econometrics 23, 37–61.CrossRefGoogle Scholar
Tukey, J. W. (1958) Bias and Confidence in not-quite large samples. Annals of Mathematical Statistics 29, 614.Google Scholar