Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T19:55:14.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Credibility Models with Time-Varying Trend Components

Published online by Cambridge University Press:  29 August 2014

Johannes Ledolter ,
Stuart Klugman  and
Chang-Soo Lee
Johannes Ledolter
Affiliation:
Department of Statistics and Actuarial Science, Department of Management Sciences, The University of Iowa, Iowa City, IA 52242
Stuart Klugman
Affiliation:
College of Business and Public Administration, Drake University. Des Moines, IA 50311
Chang-Soo Lee
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242
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.

Traditional credibility models have treated the process generating the losses as stable over time, perhaps with a deterministic trend imposed. However, there is ample evidence that these processes are not stable over time. What is required is a method that allows for time-varying parameters in the process, yet still provides the shrinkage needed for sound ratemaking. In this paper we use an automobile insurance example to illustrate how this can be accomplished.

Keywords

CredibilityKalman filtershrinkage estimationtime seriestrend components.
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 21 , Issue 1 , April 1991 , pp. 73 - 91
Copyright
Copyright © International Actuarial Association 1991

References

REFERENCES

Abraham, B. and Ledolter, J. (1983) Statistical Methods for Forecasting. New York: Wiley.CrossRefGoogle Scholar
Abraham, B. and Ledolter, J. (1986) Forecast Functions Implied by ARIMA Models and Other Related Forecast Procedures. International Statistical Review 54, 51–66.CrossRefGoogle Scholar
Ansley, C. and Kohn, R. (1985) Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions. Annals of Statistics 13, 1286–1316.CrossRefGoogle Scholar
Bailey, R.A. and Simon, L.J. (1959) An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car. Proceedings of the Casualty Actuarial Society 46, 159–164.Google Scholar
Box, G. and Jenkins, G. (1976) Time Series Analysis, Forecasting, and Control (2nd ed.). San Francisco: Holden-Day.Google Scholar
Bühlmann, H. and Straub, E. (1972) Credibility for Loss Ratios. Actuarial Research Clearing House, Number 2.Google Scholar
De Jong, P. (1988) The Likelihood for a State Space Model. Biometrika 75, 165–169.CrossRefGoogle Scholar
De Jong, P. and Zehnwirth, B. (1983) Credibility Theory and the Kalman Filter. Insurance: Mathematics and Economics 2, 281–286.Google Scholar
deVylder, F. (1981) Practical Credibility Theory with Emphasis on Optimal Parameter Estimation. ASTIN Bulletin 12, 115–131.CrossRefGoogle Scholar
deVylder, F. (1984) Practical Models in Credibility Theory, Including Parameter Estimation. In: Premium Calculation in Insurance, Devylder, F., Goovaerts, M. and Haezendonck, J., editors, Reidel.CrossRefGoogle Scholar
Garcia-Ferrer, A., Highfield, R. A., Palm, F. and Zellner, A. (1987) Macroeconomic Forecasting using Pooled International Data. Journal of Business and Economic Statistics 5, 53–67.Google Scholar
Gerber, H. and Jones, D. (1975) Credibility Formulas of the Updating Type. Transactions of the Society of Actuaries 27, 31–46.Google Scholar
Granger, C. W. J. and Newbold, P. (1976) Forecasting Transformed Series. Journal of the Royal Statistical Society, Series B 38, 189–203.Google Scholar
Hachemeister, C. (1975) Credibility for Regression Models with Applications to Trend. In Credibility: Theory and Applications, Kahn, P., ed., New York: Academic Press.Google Scholar
Harvey, A. (1984) A Unified View of Statistical Forecasting Procedures. Journal of Forecasting 3, 245–283.CrossRefGoogle Scholar
Harvey, A. and Todd, P. (1983) Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study. Journal of Business and Economic Statistics 1, 299–315.Google Scholar
Harvey, A. and Fernandes, C. (1989) Time Series Models for Insurance Claims. Journal of the Institute of Actuaries 116, Part 3, 513–528.CrossRefGoogle Scholar
Jazwinski, A. (1970) Stochastic Processes and Filtering Theory. New York: Academic Press.Google Scholar
Klugman, S. (1987) Credibility for Classification Ratemaking via the Hierarchical Linear Model. Proceedings of the Casualty Actuarial Society 74, 272–321.Google Scholar
Kohn, R. and Ansley, C. (1986) Estimation, Prediction, and Interpolation for ARIMA Models with Missing Data. Journal of the American Statistical Association 81, 751–761.CrossRefGoogle Scholar
Ledolter, J., Klugman, S. and Lee, C. S. (1989) Credibility Models with Time-Varying Trend Components, Technical Report 159, Department of Statistics and Actuarial Science, University of Iowa.Google Scholar
Lee, C.S. (1991) Time Series Models for the Credibility Estimation of Insurance Premiums, unpublished Ph.D. dissertation (forthcoming), Department of Statistics and Actuarial Science, University of Iowa.Google Scholar
Meinhold, R. and Singpurwalla, N. (1983) Understanding the Kalman Filter. The American Statistician 37, 123–127.Google Scholar
Meyers, G. (1984) Empirical Bayesian Credibility for Workers' Compensation Classification Ratemaking. Proceedings of the Casualty Actuarial Society 71, 96–121.Google Scholar
Meyers, G. and Schenker, N. (1983) Parameter Uncertainty in the Collective Risk Model. Proceedings of the Casualty Actuarial Society 70, 111–143.Google Scholar
Mowbray, A. (1914) How Extensive a Payroll is Necessary to Give a Dependable Pure Premium? Proceedings of the Casualty Actuarial Society 1, 24–30.Google Scholar
Neuhaus, W. (1987) Early Warning. Scandinavian Actuarial Journal, 128–156.CrossRefGoogle Scholar
Schweppe, F. (1965) Evaluation of Likelihood Functions for Gaussian Signals. IEEE Trans. Inf. Theory 11, 61–70.CrossRefGoogle Scholar
Sundt, B. (1981) Recursive Credibility Estimation. Scandinavian Actuarial Journal, 3–21.CrossRefGoogle Scholar
Swamy, P. A. V. B. (1971) Statistical Inference in Random Coefficient Regression Models. New York: Springer.CrossRefGoogle Scholar
Zellner, A. and Hong, C. (1989) Forecasting International Growth Rates Using Bayesian Shrinkage and other Procedures. Journal of Econometrics 40, 183–202.CrossRefGoogle Scholar