Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-24T00:43:46.587Z Has data issue: false hasContentIssue false

Note Concerning the Distribution Function of the Total Loss Excluding the Largest Individual Claims

Published online by Cambridge University Press:  29 August 2014

Hans Ammeter*
Affiliation:
Zurich, Switzerland
Rights & Permissions [Opens in a new window]

Extract

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.

The theory of extreme values is a special branch of mathematical statistics and was mainly treated by E. J. Gumbel [4]). This theory has only been applied in a few cases to problems in the insurance business. The first practical application to insurance known to the author of the present paper is due to A. Thépaut who has invented a new reinsurance system called ECOMOR [5]. According to this system the reinsurer covers the excess risk for the m largest claims and the ceding company retains an amount equal to the (m + I) largest claim. The credit for having pointed out the importance of the theory of extreme values belongs to R. E. Beard [1]. Recently E. Franckx [3] has found a most remarkable result by disclosing the general form of the distribution for the largest claim occurring in a certain accounting period.

The present paper starts from the consideration that not only is the distribution of major claims, which might be eliminated by means of reinsurance, of interest to an insurer but also the distribution of the remaining total loss after excluding the largest claims. The nature of this distribution is important not only in connection with stability and security, but also for statistical investigations of the observed claim ratio. The credibility of such an investigation might be greatly improved if a suitable number of major claims were excluded. To simplify matters, the present paper considers the case where only the largest claim is excluded.

Type
Papers
Copyright
Copyright © International Actuarial Association 1964

References

LIST OF REFERENCES

[1]Beard, Robert Eric: Some Notes on the Statistical Theory of Extreme Values. The ASTIN Bulletin, Vol. III, Part I, 1963.Google Scholar
[2]Benktander, Gunnar, und Segerdahl, Carl-Otto: On the Analytical Representation of Claim Distributions with Special Reference to Excess of Loss Reinsurance. Transactions of the XVIth International Congress of Actuaries, Brussels 1960.Google Scholar
[3]Franckx, Edouard: Sur la fonction de distribution du sinistre le plus éléve. The ASTIN Bulletin, Vol. II, Part III, 1963.Google Scholar
[4]Gumbel, E. J.: Statistics of Extremes. Columbia University Press, New York 1958.CrossRefGoogle Scholar
[5]Thépaut, André: Le traité d'excédent du coût moyen relatif (Ecomor). Bulletin Trimestriel de l'lnstitut des Actuaires Franҁais, No 192, Septembre 1950.Google Scholar