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On Changing the Parameter of Exponential Smoothing in Experience Rating

Published online by Cambridge University Press:  29 August 2014

Heikki Bonsdorff
Heikki Bonsdorff*
Affiliation:
Pohjola Insurance Company Ltd., Helsinki, Finland
*
Pohjola Insurance Company Ltd., Lapinmäentie 1, 00300 Helsinki, Finland.
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Abstract

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We consider exponential smoothing Yn = αXn + (1 − α)Yn−1, 0 < α < 1, in experience rating. Here the premium Yn is determined by the policy's own claims history (Xn). In order to uniformize the fluctuation of premiums, it is appropriate to use a bigger α for the big policies than for the small ones. When the size of the policy changes with time, a need arises to change α correspondingly. It has recently been shown that changing based on the size of the premiums Yn may lead to too low a tariff level. This result is presented here and illustrated by means of simulation. Further, some general results are given how the changing can be made without a decline in the tariff level. The results are applied to a tariff system in which the linking of the smoothing parameter to the size of the policy is particularly motivated.

Keywords

Exponential smoothingadaptive smoothingexperience ratingMarkov chainsbig claimsworkers' compensation insurance
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 2 , November 1990 , pp. 191 - 200
Copyright
Copyright © International Actuarial Association 1990

References

[1]Bonsdorff, H. (1989) A comparison of the ordinary and a varying parameter exponential smoothing. J. Appl. Prob. 26, 784–792.CrossRefGoogle Scholar
[2]Brown, R. G. (1963) Smoothing, Forecasting and Prediction of Discrete Time Series. Prentice Hall, Englewood Cliffs, N.J.Google Scholar
[3]Gerber, H.U. and Jones, D.A. (1975) Credibility formulas of the updating type. In: Credibility: Theory and Applications, (ed. Kahn, P.M.), pp. 89–105. Academic Press, New York.Google Scholar
[4]Kremer, E. (1982) Exponential smoothing and credibility theory. Insurance: Math. Econ. 1, 213–217.Google Scholar
[5]Rantala, J. (1984) An application of stochastic control theory to insurance business. Acta Universitatis Tamperensis, A, 164, Tampere.Google Scholar
[6]SIMBERG, H. (1964) Individuelle Prämienregelung, eine Art des “Experience Rating”. Trans. 17th Internat. Congr. of Actuaries, London Edinburgh 3, 650–659.Google Scholar
[7]Sundt, B. (1988) Credibility estimators with geometric weights. Insurance: Math. Econ. 7, 113–122.Google Scholar