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The Reinsurer's Monopoly and the Bowley Solution

Published online by Cambridge University Press:  29 August 2014

Fung-Yee Chan  and
Hans U. Gerber
Fung-Yee Chan
Affiliation:
University of Winnipeg
Hans U. Gerber
Affiliation:
University of Lausanne
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Abstract

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The reinsurer has a monopoly in the following sense: He will select a random variable P that determines the reinsurance premiums. The first insurer can purchase a payment of R (a random variable) for a premium of π = E[PR]. For known P, the first insurer chooses R to maximize his expected utility. Knowing this, i.e., the demand for reinsurance as a function of P, the reinsurer chooses P to maximize his utility. The resulting pair (P, R) is called the Bowley solution. Assuming exponential, quadratic and/or linear utility functions, some explicit results are obtained.

Keywords

Utility functionreinsuranceBowley solution
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 15 , Issue 2 , November 1985 , pp. 141 - 148
Copyright
Copyright © International Actuarial Association 1985

References

Bühlmann, H. (1968) Marktverhalten unter Risiko—das Deckungsmonopol. Transactions of the 18th International Congress of Actuaries 379–392.Google Scholar
Bühlmann, H. (1980) An economic premium principle. Astin Bulletin 11, 52–60.CrossRefGoogle Scholar
Deprez, O. and Gerber, H. U. (1985) On Convex Principles of Premium Calculation. Insurance: Mathematics & Economics 4, 179–189.Google Scholar
Gerber, H. U. (1984) Chains of Reinsurance. Insurance: Mathematics & Economics 3, 43–48.Google Scholar