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A General Bound for the Net Premium of the Largest Claims Reinsurance Covers

Published online by Cambridge University Press:  29 August 2014

Erhard Kremer*
Affiliation:
Universität Hamburg
*
Institut für Mathematische Stochastik, Universität Hamburg, D-2000 Hamburg 13, Germany
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Abstract

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For a general class of reinsurance treaties the author gives an upper bound for the net premium. This result can be seen as the counterpart to a premium bound for the classical stop-loss reinsurance cover (see Bowers, 1969). For some special cases some preliminary work can be found in Kremer (1983).

Type
Articles
Copyright
Copyright © International Actuarial Association 1988

References

Ammeter, H. (1964) The rating of the “Largest claim” reinsurance covers. Quarterly Letter Jubilee Number 79109.Google Scholar
Benktander, G. (1978) Largest claims reinsurance (LCR). A quick method to calculate LCR-risk rates from excess of loss risk rates. ASTIN Bulletin 10, 5458.CrossRefGoogle Scholar
Berliner, B. (1972) Correlations between excess of loss reinsurance covers and reinsurance of the n largest claims. ASTIN Bulletin 6, 260275.CrossRefGoogle Scholar
Bowers, N. L. (1969) An upper bound on the stop-loss net premium. Transactions of the Society of Actuaries 21, 211217.Google Scholar
Ciminelli, E. (1976) On the distribution of the highest claims and its application to the automobile insurance liability. Transactions of the 20-th International Congress of Actuaries 501517.Google Scholar
David, H. A. (1980) Order Statistics. John Wiley, New York.Google Scholar
Kremer, E. (1982) Rating of the largest claims and ECOMOR reinsurance treaties for large portfolios. ASTIN Bulletin 13, 4756.CrossRefGoogle Scholar
Kremer, E. (1983) Distribution-free upper bounds on the premiums of the LCR and ECOMOR treaties. Insurance: Mathematics and Economics 2, 209213.Google Scholar
Kremer, E. (1984) An asymptotic formula for the net premium of some reinsurance treaties. Scandinavian Actuarial Journal 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. (1986a) Simple formulas for the premiums of the LCR and ECOMOR treaties under exponential claim sizes. Blätter der deutschen Gesellschaft für Versicherungsmathematik XVII, 237243.Google Scholar
Kremer, E. (1986b) Recursive calculation of the net premium for largest claims reinsurance covers. ASTIN Bulletin 16, 101108.CrossRefGoogle Scholar
Kremer, E. (1988) Reinsurance premiums under generalized claim number distributions. To appear in the Transactions of the 23rd International Congress of Actuaries, Helsinki 1988.Google Scholar
Kupper, J. (1971) Contributions to the theory of the largest claims cover. ASTIN Bulletin 6, 134146.CrossRefGoogle Scholar
Lehmann, E. L. (1983) Theory of Point Estimation. John Wiley, New York.CrossRefGoogle Scholar
Loève, M. (1963) Probability Theory. Van Nostrand, New York.Google Scholar