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Credibility and Persistency

Published online by Cambridge University Press:  29 August 2014

Virginia R. Young
Virginia R. Young*
Affiliation:
University of Wisconsin-Madison
*
School of Business, Grainger Hall, University of Wisconsin-Madison, Madison, WI, USA53706
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Abstract

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Policyholders often decide to buy, renew, or cancel insurance based on the premium charged by the insurer compared with what they expect their claims will be. It is important for actuaries to consider the persistency of policyholders because the financial well-being of the insurer depends on spreading its risk over a large book of business. We use statistical decision theory to develop premium formulas that account for the past experience of a given policyholder, the experience of the entire collection of policyholders, and the likelihood of the policyholder renewing with or buying from a given insurer, that is, persistency.

We assume that the persistency of policyholders depends on the arithmetic difference between the premium charged and their anticipated claims. We extend the work of Taylor (1975) in which he obtains linear credibility formulas by minimizing loss functions that incorporate the persistency of policyholders. We consider Taylor's loss functions and other objective functions, including those that account for the amount of business the insurer writes or renews.

Keywords

Credibilitypersistencystatistical decision theory
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 53 - 69
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. (1970) Mathematical Models in Risk Theory. Springer-Verlag, New York.Google Scholar
Bühlmann, H. and Straub, E. (1970) Glaubwürdigkeit für Schadensätze. Mitteilungen der Vereinigung Schweizerischer Versicherungs-Mathematiker 70, 111–133.Google Scholar
Gerber, H. U. (1980), Credibility for Esscher premiums. Mitteilungen der Vereinigung Schweizerischer Versicherungs-Mathematiker 80, 307–312.Google Scholar
Goovaerts, M.J. and Hoogstad, W.J. (1987) Credibility Theory. Surveys of Actuarial Studies, No. 4, Nationale-Nederlanden, Rotterdam, The Netherlands.Google Scholar
Jewell, W. S. (1974a) Credibility is exact Bayesian for exponential families. ASTIN Bulletin 8, 77–90.CrossRefGoogle Scholar
Jewell, W. S. (1974b) Regularity conditions for exact credibility. ASTIN Bulletin 8, 336–341.CrossRefGoogle Scholar
Klugman, S.A. (1992) Bayesian Statistics in Actuarial Science with Emphasis on Credibility. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Kremer, E. (1982) Credibility theory for some evolutionary models. Scandinavian Actuarial Journal, 129–142.CrossRefGoogle Scholar
Ledolter, J., Klugman, S. and Lee, C.S. (1991), Credibility models with time-varying trend components, ASTIN Bulletin, 21: 73–86.CrossRefGoogle Scholar
Morewood, F. G. (1992) Planning and control issues. In Group Insurance (ed. Bluhm, W.F.), chapter 34, ACTEX Publications, Winsted, Connecticut.Google Scholar
Norberg, R. (1992) Linear estimation and credibility in continuous time. ASTIN Bulletin 22, 149–165.CrossRefGoogle Scholar
Panjer, H.H. and Li, D.X. (1994) Credibility models: An estimating function approach. Working paper.Google Scholar
Sundt, B. (1983) Credibility models allowing durational effects. Mitteilungen der Vereinigung Schweizerischer Versicherungs-Mathematiker 83, 63–87.Google Scholar
Taylor, G.C. (1975) Credibility under conditions of imperfect persistency. In Credibility: Theory and Applications (ed. Kahn, P.M.), pp. 391–400, Academic Press, New York.Google Scholar
Venter, G. (1990) Credibility. In Foundations of Casualty Actuarial Science, Casualty Actuarial Society, New York.Google Scholar
Willmot, G.E. (1994) Introductory Credibility Theory. Institute of Insurance and Pension Research, University of Waterloo, Waterloo, Ontario.Google Scholar