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In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the probability distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear.
KeywordsParametric utility Hyperbolic absolute risk aversion (HARA) Exponential utility Power utility
We are grateful to Sjak Smulders and Peter Wakker for helpful discussions, and to the referee for constructive comments. This research was funded in part by the JSPS under grant C-22530177 (Ikefuji) and by the NWO under grant Vidi-2009 (Laeven). An earlier version of this article was circulated under the title ‘Burr utility’.
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
- Abramowitz, M., Stegun, I. A. (eds) (1964) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New YorkGoogle Scholar
- Arrow K. J. (1971) Essays in the theory of risk bearing. North-Holland, AmsterdamGoogle Scholar
- Box G. E. C., Tiao G. C. (1973) Bayesian inference in statistical analysis. Addison-Wesley, BostonGoogle Scholar
- Chiappori, P.-A., & Paiella, M. (2008). Relative risk aversion is constant: Evidence from panel data. Discussion paper no. 5/2008. Department of Economic Studies, University of Naples ‘Parthenope’, Naples.Google Scholar
- de Finetti B. (1952) Sulla preferibilità. Giornale degli Economisti e Annali di Economia 11: 685–709Google Scholar
- Eeckhoudt L., Gollier C. (1995) Risk: Evaluation, management and sharing. Harvester Wheatsheaf, HertfordshireGoogle Scholar
- Friend I., Blume M. E. (1975) The demand for risky assets. American Economic Review 65: 900–922Google Scholar
- Gerber H. U. (1979) An introduction to mathematical risk theory. S.S. Huebner Foundation Monograph. Irwin, Homewood, ILGoogle Scholar
- Gollier C. (2001) The economics of risk and time. MIT Press, Cambridge, MAGoogle Scholar
- Ikefuji, M., Laeven, R. J. A., Magnus, J. R., & Muris, C. (2011). Weitzman meets Nordhaus: Expected utility and catastrophic risk in a stochastic economy-climate model. Working paper, Tilburg University.Google Scholar
- Johnson N. L., Kotz S., Balakrishnan N. (1995) Continuous univariate distributions (2nd ed.,Vol. 2). Wiley, New YorkGoogle Scholar
- Subbotin M. Th. (1923) On the law of frequency of error. Mathematicheskii Sbornik 31: 296–301Google Scholar