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Calculation of Price Equilibria for Utility Functions of the HARA Class

Published online by Cambridge University Press:  29 August 2014

Markus Lienhard
Markus Lienhard*
Affiliation:
Université de Lausanne
*
Université de Lausanne, HEC, CH-1015 Lausanne, Switzerland
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Abstract

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We explicitly calculate price equilibria for power and logarithmic utility functions which—together with the exponential utility functions—form the so-called HARA (Hyperbolic Absolute Risk Aversion) class.

A price equilibrium is economically admissible in the market which is a closed system. Furthermore it is on the one side individually optimal for each participant of the market (in the sense of maximal expected utility), on the other side it is a Pareto optimum and thus collectively optimal for the market as a whole.

Keywords

Risk exchangePrice equilibriumUtility functionPareto optimalityRisk aversion
Type
Astin Competition 1985: Prize-Winning Papers and Other Selected Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue S1 , April 1986 , pp. S91 - S97
Copyright
Copyright © International Actuarial Association 1986

References

Bühlmann, H. (1980) An Economic Premium Principle. ASTIN Bulletin 11 (1), 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984) The General Economic Premium Principle. ASTIN Bulletin 14 (1).CrossRefGoogle Scholar
Bühlmann, H. and Jewell, W. S. (1979) Optimal Risk Exchanges. ASTIN Bulletin 10 (3), 249.CrossRefGoogle Scholar