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An Economic Index of Riskiness

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Author Info
Robert J. Aumann
Roberto Serrano

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Abstract

Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a "duality" axiom that, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is positively homogeneous, continuous, and subadditive; respects first- and second-order stochastic dominance; and for normally distributed gambles is half of variance/mean. Examples are calculated, additional properties are derived, and the index is compared with others. (c) 2008 by The University of Chicago. All rights reserved..

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File URL: http://www.journals.uchicago.edu/doi/pdf/10.1086/591947
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Publisher Info
Article provided by University of Chicago Press in its journal Journal of Political Economy.

Volume (Year): 116 (2008)
Issue (Month): 5 (October)
Pages: 810-836
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Handle: RePEc:ucp:jpolec:v:116:y:2008:i:5:p:810-836

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  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March. [Downloadable!] (restricted)
  2. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Blackwell Publishing, vol. 36(107), pages 335-46, July. [Downloadable!] (restricted)
  3. Palacios-Huerta, Ignacio & Serrano, Roberto, 2006. "Rejecting small gambles under expected utility," Economics Letters, Elsevier, vol. 91(2), pages 250-259, May. [Downloadable!] (restricted)
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  4. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July. [Downloadable!] (restricted)
  5. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July. [Downloadable!] (restricted)
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September. [Downloadable!] (restricted)
  7. Tobin, James, 1969. "Comment on Borch and Feldstein," Review of Economic Studies, Blackwell Publishing, vol. 36(105), pages 13-14, January. [Downloadable!] (restricted)
  8. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
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