Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-11T21:50:27.697Z Has data issue: false hasContentIssue false

On Changing the Parameter of Exponential Smoothing in Experience Rating

Published online by Cambridge University Press:  29 August 2014

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

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.

Type
Workshop
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, 784792.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. 89105. Academic Press, New York.Google Scholar
[4]Kremer, E. (1982) Exponential smoothing and credibility theory. Insurance: Math. Econ. 1, 213217.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, 650659.Google Scholar
[7]Sundt, B. (1988) Credibility estimators with geometric weights. Insurance: Math. Econ. 7, 113122.Google Scholar