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Dual approaches to the analysis of risk aversion

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  • Chambers, Robert G
  • Quiggin, John

Abstract

Dual approaches have proved their value in many areas of economic analysis. Until recently, however, they have been virtually ignored in the analysis of choice under uncertainty.In this paper, we present a dual formulation of choice under uncertainty based on a few simple assumptions about preferences, namely, continuity, monotonicity and convexity of preference sets. Particular emphasis is given to showing that the additive separability restriction, key to expected-utility theory, on preferences can be dropped with little loss of analytic power for a broad class of choice problems.

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Bibliographic Info

Paper provided by University of Queensland, School of Economics in its series Risk and Sustainable Management Group Working Papers with number 151175.

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Date of creation: 15 Jun 2006
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Handle: RePEc:ags:uqsers:151175

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Keywords: Risk and uncertainty; Risk and Uncertainty; D81;

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References

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  1. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-36, February.
  2. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  3. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  4. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
  5. Milgrom, Paul, 1994. "Comparing Optima: Do Simplifying Assumptions Affect Conclusions?," Journal of Political Economy, University of Chicago Press, vol. 102(3), pages 607-15, June.
  6. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
  7. Brennan, M. J. & Kraus, A., 1976. "The Geometry of Separation and Myopia," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(02), pages 171-193, June.
  8. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  9. Epstein, Larry G. & Zin, Stanley E., 1990. "'First-order' risk aversion and the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 387-407, December.
  10. Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics.
  11. Milne, Frank, 1979. "Consumer Preferences, Linear Demand Functions and Aggregation in Competitive Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 46(3), pages 407-17, July.
  12. Feder, Gershon, 1977. "The impact of uncertainty in a class of objective functions," Journal of Economic Theory, Elsevier, vol. 16(2), pages 504-512, December.
  13. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  14. Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
  15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  16. Quiggin, John & Chambers, Robert G, 1998. "Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 121-37, November.
  17. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
  18. Lwebel Arthur & Perraudin William, 1995. "A Theorem on Portfolio Separation with General Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 624-626, April.
  19. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer, vol. 11(3), pages 629-641.
  20. Peleg, Bezalel, 1975. "Efficient random variables," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 243-252.
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Citations

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Cited by:
  1. James Roumasset, 2010. "Wither The Economics of Agricultural Development?," Working Papers 2010-03, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
  2. Chambers, Robert G. & Quiggin, John, 2005. "Linear-risk-tolerant, invariant risk preferences," Economics Letters, Elsevier, vol. 86(3), pages 303-309, March.
  3. Robert Chambers & Rolf Färe, 2008. "A “calculus” for data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 30(3), pages 169-175, December.
  4. Trino-Manuel Niguez & Ivan Paya & David Peel & Javier Perote, 2013. "Higher-order moments in the theory of diversification and portfolio composition," Working Papers 18297128, Lancaster University Management School, Economics Department.

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