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The Calculation Of A Fluctuation Loading For An Excess Of Loss Cover

Published online by Cambridge University Press:  29 August 2014

Gunnar Benktander
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A diminishing number of Reinsurers still seem to work with percentage loadings which are applied with more or less sophistication to the pure risk premium rate.

A more sensible approach is to study the distribution of the total claims amount of the layer reinsured (standard deviation, variance, skewness).

In practice this distribution is not known and we have to work with estimates E* and σ*2 of the first moment which is the pure risk premium (E) and of the second central moment (σ2). Because of the positive skewness of the distribution, E* will fall below E in more than half of the cases and sometimes considerably below.

One security loading principle could be to add a proportion k of σ* to E* in such a way that

If ε is put equal to 0.25 this reflects our wish to ensure that our security loaded rates are too low only in 25% of the cases. A σ- loading here emerges as a result of the statistical uncertainty.

If we analyse the result fluctuations we are led to apply a variance loading (1), which can be interpreted as a price for capacity (2). (See also discussion contributions by B. Ajne, G. Benktander, G. Berger, H. Bühlmann; Transactions of the Congress, 5, Oslo 1972, p. 169 ff.)

An underwriter who is confronted with two portfolios having the same first and second moments should, if conditions are the same, prefer the one with the lower third moment. A special loading for skewness is thus indicated.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 8 , Issue 3 , September 1975 , pp. 272 - 278
Copyright
Copyright © International Actuarial Association 1975

References

[1]Benktander, G., Some Aspects on Reinsurance Profits and Loadings. The ASTIN-Bulletin, Vol. V, Part 3.Google Scholar
[2]Benktander, G., A Note on Profit Margin and Insurance Market Capacity. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 1970, 70. Band, Heft 1.Google Scholar
[3]Benktander, G., and Berliner, B., A New Approach to the Characterization of Risk (to be published).Google Scholar
[4]Benktander, G.and Segerdahl, C. O., On the Analytical Representation of Claims Distribution with Special Reference to Excess of Loss Reinsurance. Transactions of the XVIth International Congress of Actuaries, Brussels, 1960, Vol. I p.626 ff.Google Scholar
[5]Benktander, G., Schadenverteilung nach Grösse in der Nichtlebenversicherung. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 1970, 70. Band, Heft 2.Google Scholar