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On the Rating of a Special Stop Loss Cover

Published online by Cambridge University Press:  29 August 2014

Gunnar Benktander
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Stop Loss reinsurance has attracted the interest of ASTIN members for years. May I recall the paper of Borch [1] in which he demonstrates some optimality qualities of the stop loss reinsurance from the ceding company's point of view, the contribution of Kahn [2] and the paper of Pesonen [3]. I also mention the paper of Esscher [4] and Verbeek's contribution [5]. Going back to the pre-ASTIN days we find a paper of Dubois [6].

The rating problems have been dealt with by several authors. Let me recall the rating formula worked out by a group of Dutch Actuaries some 20 years ago. This was based on the assumption that the mean and the standard deviation were known. Based on Chebycheff's inequality an approximation formula was worked out which, of course, was heavily on the safe side.

Even younger members of ASTIN are probably familiar with the studies made in the early sixties by a group of Swedish Actuaries, the results of which were presented by Bohman at the Actuarial Congress in London in 1964. Partly based on this, Bühlmann worked out some tables which he used for rating purposes.

My present contribution to the subject may not justify the above reviews, particularly as I will deal with a very special retention situation which a practical underwriter will rightly not accept, namely a stop-loss point as low as equal to the mean value of the distribution.

My excuse for this is that the formula deduced is very handy and that it is of value to the underwriter to know the stop loss risk rate also at this low level.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 9 , Issue 1-2 , January 1977 , pp. 33 - 41
Copyright
Copyright © International Actuarial Association 1977

References

REFERENCES

[1]Borch, K., “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, XVIth International Congress of Actuaries, Bruxelles, 1960.Google Scholar
[2]Kahn, P. M., “Some Remarks on a Recent Paper by Borch”, ASTIN-Kolloquium Rättvik, ASTIN-Bulletin, Vol. 1, Part V, 1961.Google Scholar
[3]Pesonen, K., “On Optimal Properties of the Stop Loss Reinsurance”, ASTIN-Bulletin, Vol. IV, Part II, 1067.Google Scholar
[4]Esscher, , “Some Problems connected with the Calculation of Stop Loss Premiums for large Portfolios”, Skandinaviske Aktuarietidskrift, 1965, a summary of which was published in the ASTIN-Bulletin.Google Scholar
[5]Verbeek, H., “On Optimal Reinsurance”, ASTIN-Bulletin, Vol. IV, Part 1, 1960.Google Scholar
[6]Dubois, , “Contribution à l'étude de la réassurance”, Transactions New York, 1037.Google Scholar