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Pareto Optimal Risk Exchanges and a System of Differential Equations: a Duality Theorem

Published online by Cambridge University Press:  29 August 2014

Erich Wyler
Erich Wyler*
Affiliation:
ETH Zürich, Switzerland
*
Anna-Heer-Strasse 28, CH-8057 Zürich, Switzerland.
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Abstract

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This article, based on a result of Borch and an extension of Bühlmann, gives a complete characterization of Pareto optimal risk exchanges by a system of differential equations linking the derivate of agents contributions to their risk aversion coefficients.

Keywords

Pareto optimal risk exchangeBernoulli utility functionabsolute risk aversionsystem of differential equations
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 1 , April 1990 , pp. 23 - 31
Copyright
Copyright © International Actuarial Association 1990

References

REFERENCES

Borch, K. (1960) The Safety Loading of Reinsurance Premiums. Skandinavisk Aktuarictidskrift 43, 163–184.Google Scholar
Bühlmann, H. (1980) An Economic Premium Principle. ASTIN Bulletin 11, 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984) The General Economic Premium Principle. ASTIN Bulletin 15, 13–21.CrossRefGoogle Scholar
Lienhard, M. (1986) Calculation of Price Equilibria for Utility Functions of the HARA class. ASTIN Bulletin 17, 91–97.CrossRefGoogle Scholar
Pratt, J. W. (1964) Risk Aversion in the Small and in the Large. Econometrica 32, 122–136.CrossRefGoogle Scholar