Aversion to one risk in the presence of others
- John W. Pratt
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The more risk-averse of two individuals need not have the smaller certainty equivalent for a risk \~x if another risk or combination of risks w is present. It is shown that he must, however, if either individual's conditional certainty equivalent for x is increasing in w. For independent risks, this condition follows immediately if either individual is decreasingly risk-averse, giving a natural proof of a known result. Another short proof of this result and necessary and sufficient conditions in the independent case are give. For multivariate utilities, the corresponding results do not hold, but it is proved simply that any mixture of decreasingly risk-averse utilities is decreasingly risk-averse. Also touched upon are risk aversion's relation to generalized means, concave composition, risk sharing, and interest rates, the application of the results to discounting under uncertainty and selection of investment level, and their connection to singly crossing distributions, noise, and dominance.
- Bawa, V. S. (1982). Stochastic Dominance: A Research Bibliography. Management Science 28, 698–712.
- Brascamp, H. J., & Lieb, E. H. (1975). Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma. In A.M. Arthurs, (ed.), Functional Integration and Its Applications. Oxford: Clarendon Press.
- Diamond, P. A. & Rothschild, M. (1978). Uncertainty in Economics: Readings and Exercises. New York: Academic Press.
- Diamond, P. A. & Stiglitz, J. E. (1974). Increases in Risk and in Risk Aversion. Journal of Economic Theory 8, 337–360.
- Hardy, G. H., Littlewood, J. E. & Pólya, G. (1934). Inequalities. Cambridge: University Press.
- Hart, O. D. (1975). Some Negative Results on the Existence of Comparative Statics Results in Portfolio Theory. Review of Economic Studies 42, 615–622.
- Kihlstrom, R. E., Rome, D. & Williams, S. (1981) Risk Aversion with Random Initial Wealth. Econometrica 49, 911–921.
- Nachman, D. C. (1979). On the Theory of Risk Aversion and the Theory of Risk. Journal of Economic Theory 21, 317–335.
- Nachman, D. C. (1980). Preservation of ‘More Risk Averse’ Under Expectations. Unpublished Working Paper, Columbia University.
- Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Econometrica 32, 122–136.
- Pratt, J. W. (1984). Remarks on Some Stronger Measures of Risk Aversion. Unpublished Working Paper, Harvard University.
- Pratt, J. W. (1986). Multiattribute Utility and Derived Utility. In Y. Sawaragi, K. Inoue and H. Nakayama, (eds.), Toward Interactive and Intelligent Decision Support Systems (Proceedings of the Seventh International Conference on Multiple Criteria Decision Making, Kyoto, Japan).
- Pratt, J. W. & Zeckhauser, R. (1987). Proper Risk Aversion. Econometrica, 55, 143–154.
- Pratt, J. W. & Zeckhauser, R. (1988). The Impact of Risk Sharing on Efficient Decision. Journal of Risk and Uncertainty, forthcoming.
- Ross, S. A. (1974). On the Economic Theory of Agency and the Principle of Similarity. In M. S. Balch, D. L. McFadden and S. Y. Wu, (eds.), Essays on Economic Behavior Under Uncertainty. North-Holland American Elsevier.
- Ross, S. A. (1981). Some Stronger Measures of Risk Aversion in the Small and the Large with Applications. Econometrica 49, 621–638.
- Schlaifer, R. (1971). Computer Programs for Elementary Decision Analysis, Boston: Division of Research, Harvard University Graduate School of Business Administration.
- Strassen, V. (1965). The Existence of Probability Measures with Given Marginals. Annals of Mathematical Statistics 36, 423–439.
- Vickson, R. G. (1977). Stochastic Dominance Tests for Decreasing Absolute Risk-Aversion II: General Random Variables. Management Science 23 478–489.
- Wilson, R. The Theory of Syndicates. (1968). Econometrica 36, 119–132.
- Aversion to one risk in the presence of others
Journal of Risk and Uncertainty
Volume 1, Issue 4 , pp 395-413
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- risk aversion
- certainty equivalent
- multivariate utilities
- independent risks
- comparative concavity
- multiple risks
- Industry Sectors
- John W. Pratt (1)
- Author Affiliations
- 1. Harvard University, USA