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A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover

Published online by Cambridge University Press:  29 August 2014

Raoul M. Berglund*
Affiliation:
Department of Mathematics, Åbo Akademi University
*
Åbo Akademi University, Department of Mathematics, Fänriksgatan 3 B, 20500 Åbo, Finland
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Abstract

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In the present paper the author gives net premium formulae for a generalized largest claims reinsurance cover. If the claim sizes are mutually independent and identically 3-parametric Pareto distributed and the number of claims has a Poisson, binomial or negative binomial distribution, formulae are given from which numerical values can easily be obtained. The results are based on identities for compounded order statistics.

Type
Workshops
Copyright
Copyright © International Actuarial Association 1998

References

REFERENCES

Abramowitz, M. and Stegun, I. (1972) Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables. Dover, New York.Google Scholar
Ammeter, H. (1964a) Note concerning the distribution function of the total loss excluding the largest individual claims. ASTIN Bulletin 3, 132143.CrossRefGoogle Scholar
Ammeter, H. (1964b) The rating of “largest claim” reinsurance covers. Quarterly letter from the Allgemeene Reinsurance Companies, Jubilee number 9, 517.Google Scholar
Berlinger, B. (1972) Largest claims reinsurance (LCR): A quick method to calculate LCR-risk rates from excess of loss risk rates. ASTIN Bulletin 10, 5458.Google Scholar
Ciminelli, E. (1976) On the distribution of the highest claims and its application to the automobile insurance liability. Transactions of the 20th International Congress of Actuaries, 501517.Google Scholar
David, H.A. (1970) Order Statistics. John Wiley & Sons, New York.Google Scholar
Daykin, C.D., Pentikäinen, T. and Pesonen, M. (1994) Practical Risk Theory for Actuaries. Chapman & Hall, London.Google Scholar
Kremer, E. (1982) Rating of largest claims and ECOMOR reinsurance treaties for large portfolios. ASTIN Bulletin 13, 4756.CrossRefGoogle Scholar
Kremer, E. (1984) An asymptotic formula for the net premium of some reinsurance treaties. Scandinavian Actuarial Journal 1984, 1122.CrossRefGoogle Scholar
Kremer, E. (1985) Finite formulae for the premium of the general reinsurance treaty based on ordered claims. Insurance: Mathematics and Economics 4, 233238.Google Scholar
Kremer, E. (1986) Simple formulas for the premiums of the LCR and ECOMOR treaties under exponential claim sizes. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 17, 457469.Google Scholar
Kremer, E. (1988a) Rückversicherungsprämien unter Verallgemeinerten Schadenzahlverteilungen. Transactions of the 23rd International Congress of Actuaries 7379.Google Scholar
Kremer, E. (1988b) A general bound for the net premium of the largest claims reinsurance covers. ASTIN Bulletin 18, 6978.CrossRefGoogle Scholar
Kupper, J. (1971) Contributions to the theory of the largest claim cover. ASTIN Bulletin 6, 134146.CrossRefGoogle Scholar
Rytgaard, M. (1990) Estimation in the Pareto distribution. ASTIN Bulletin 20, 201216.CrossRefGoogle Scholar