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Premium Calculation for Deductible Policies with an Aggregate Limit

Published online by Cambridge University Press:  29 August 2014

Thomas Mack
Thomas Mack*
Affiliation:
Münchener Rückversicherungs-Gesellschaft, Munich
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Abstract

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In Industrial Fire insurance an aggregate limit for the amount retained by the policyholder under a deductible policy has been agreed upon more frequently in recent times. This agreement is equivalent to a stop-loss cover on the retained loss amount. For the Poisson-lognormal model the corresponding stop-loss net premium is calculated using various methods (normal power, translated gamma, various discretisations) and the methods are compared. Finally, the influence of the model parameters is examined and it is demonstrated how a variety of parameter value combinations can be reduced to only a few rating curves.

Keywords

Deductiblesaggregate limitstop-loss premiumIndustrial Fire insurancePoisson-lognormal model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 14 , Issue 2 , October 1984 , pp. 105 - 121
Copyright
Copyright © International Actuarial Association 1984

References

REFERENCES

Beard, R. E., Pentikäinen, T. and Pesonen, E. (1969, 1977). Risk Theory. 2nd ed. Chapman and Hall: London.Google Scholar
Benckert, L.-G. (1962) The Lognormal Model for the Distribution of One Claim. ASTIN Bulletin 2, 9–23.CrossRefGoogle Scholar
Benktander, G. (1974) A Motor Excess Rating Problem: Flat Rate with Refund. ASTIN-Colloquium Turku.Google Scholar
Berger, G. (1972) Integration of the Normal Power Approximation. ASTIN Bulletin 7, 90–95.CrossRefGoogle Scholar
Bohman, H. and Esscher, F. (1963, 1964) Studies in Risk Theory With Numerical Illustrations Concerning Distribution Functions and Stop-Loss Premiums. Skandinavisk Aktuarietidskrift 46, 173–225 and 47, 1–40.Google Scholar
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1982) Risk Theory. Society of Actuaries: U.S.A.Google Scholar
Bühlmann, H., Gagliardi, B., Gerber, H. U. and Straub, E. (1977) Some Inequalities for Stop-Loss Premiums. ASTIN Bulletin 9, 75–83.CrossRefGoogle Scholar
Ferrara, G. (1971) Distributions des Sinistres Incendie Selon leur Cout. ASTIN Bulletin 6, 31–41.CrossRefGoogle Scholar
Gerber, H. U. (1980) An Introduction to Mathematical Risk Theory. Irwin: Homewood, Illinois.Google Scholar
Gerber, H. U. (1982). On the Numerical Evaluation of the Distribution of Aggregate Claims and its Stop-Loss Premiums. Insurance: Mathematics and Economics 1, 13–18.Google Scholar
Kauppi, L. and Ojantakanen, P. (1969) Approximations of the Generalized Poisson Function. ASTIN Bulletin 5, 213–226.CrossRefGoogle Scholar
Khamis, S. H. and Rudert, W. (1965) Tables of the Incomplete Gamma Function Ratio. Justus von Liebig-Verlag: Darmstadt.Google Scholar
Mack, T. (1980) Über die Aufteilung des Risikos bei Vereinbarung einer Franchise. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 14, 631–650.Google Scholar
Mack, T. (1983) The Utility of Deductibles from the Insurer's Point of View. ASTIN-Colloquium Lindau.Google Scholar
Panjer, H. H. (1980) The Aggregate Claims Distribution and Stop-Loss Reinsurance. Transactions of the Society of Actuaries 32, 523–545.Google Scholar
Pesonen, , (1969) NP-Approximation of Risk Processes. Skandinavisk Aktuarietidskrift 52, Supplement, 63–69.Google Scholar
Seal, H. L. (1979) Approximations to Risk Theory's F(x, t) by Means of the Gamma Distribution. ASTIN Bulletin 9, 213–218.CrossRefGoogle Scholar
Sterk, H.-P. (1979) Selbstbeteiligung unter risikotheoretischen Aspekten. Verlag Versicherungswirtschaft: Karlsruhe.Google Scholar
Strauss, J. (1975) Deductibles in Industrial Fire Insurance. ASTIN Bulletin 8, 378–393.CrossRefGoogle Scholar