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Comparative risk aversion when the outcomes are vectors

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Author Info
Sudhir A. Shah (Delhi School of Economics)
Abstract

Pratt (1964) and Yaari (1969) contain the classical results pertaining to the equivalence of various notions of comparative risk aversion of von Neumann-Morgenstern utilities in the setting with real-valued outcomes. Some of these results have been extended to the setting with outcomes in < n . We obtain ana-logues of the classical results in the setting with outcomes in ordered topological vector spaces when differentiability is not required, and in the setting with out-comes in ordered Hilbert spaces when differentiability is required, as is the case when we work with a vector-valued generalized notion of an Arrow-Pratt coeffi-cient.

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Paper provided by Centre for Development Economics, Delhi School of Economics in its series Working papers with number 149.

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Length: 23 pages
Date of creation: Sep 2006
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Handle: RePEc:cde:cdewps:149

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Related research
Keywords: Comparative risk aversion; vector space of outcomes; acceptance set; vector-valued risk premia; vector-valued Arrow-Pratt coefficient; Pettis integral; ordered topological vector spaces; ordered Hilbert spaces;

Find related papers by JEL classification:
C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November. [Downloadable!] (restricted)
  2. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good choice Axioms: When can many-good lotteries be treated as money lotteries?," Journal of Economic Theory, Elsevier, vol. 56(2), pages 313-337, April. [Downloadable!] (restricted)
  3. Spence, Michael & Zeckhauser, Richard J, 1972. "The Effect of the Timing of Consumption Decisions and the Resolution of Lotteries on the Choice of Lotteries," Econometrica, Econometric Society, vol. 40(2), pages 401-03, March. [Downloadable!] (restricted)
  4. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good risks: An interpretation of multivariate risk and risk aversion without the Independence axiom," Journal of Economic Theory, Elsevier, vol. 56(2), pages 338-351, April. [Downloadable!] (restricted)
  5. Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May. [Downloadable!] (restricted)
  6. Karni, Edi, 1989. "Generalized Expected Utility Analysis of Multivariate Risk Aversion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 297-305, May. [Downloadable!] (restricted)
  7. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July. [Downloadable!] (restricted)
  8. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October. [Downloadable!] (restricted)
  9. Peters, H. J. M. & Wakker, P. P., 1986. "Convex functions on non-convex domains," Economics Letters, Elsevier, vol. 22(2-3), pages 251-255. [Downloadable!] (restricted)
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