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Dual Approaches to the Analysis of Risk Aversion

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  • ROBERT G. CHAMBERS
  • JOHN QUIGGIN

Abstract

We present a dual formulation of choice under uncertainty based on a few simple assumptions about preferences. It is shown that the additive separability restriction on preferences, key to expected-utility theory, can be dropped with little loss of analytic power for a broad class of choice problems. Dual risk premiums are characterized, and it is shown that placing various invariance restrictions on them leads naturally to generalizations of the concepts of CARA, CRRA, and LRT familiar from expected-utility theory. Each of these generalizations conforms to a notion of homotheticity. Copyright (c) The London School of Economics and Political Science 2006.

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Bibliographic Info

Article provided by London School of Economics and Political Science in its journal Economica.

Volume (Year): 74 (2007)
Issue (Month): 294 (05)
Pages: 189-213

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Handle: RePEc:bla:econom:v:74:y:2007:i:294:p:189-213

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  1. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
  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.
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  7. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  8. 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.
  9. Peleg, Bezalel, 1975. "Efficient random variables," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 243-252.
  10. 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.
  11. Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics.
  12. Thibault Gadjos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," Working Papers 2002-33, Centre de Recherche en Economie et Statistique.
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  14. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
  15. 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.
  16. 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.
  17. 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.
  18. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer, vol. 11(3), pages 629-641.
  19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  20. 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.
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Cited by:
  1. Pedro Macedo & Elvira Silva & Manuel Scotto, 2014. "Technical efficiency with state-contingent production frontiers using maximum entropy estimators," Journal of Productivity Analysis, Springer, vol. 41(1), pages 131-140, February.
  2. Chambers, Robert G. & Quiggin, John, 2005. "Linear-risk-tolerant, invariant risk preferences," Economics Letters, Elsevier, vol. 86(3), pages 303-309, March.
  3. James P. Roumasset, 2010. "Wither the Economics of Agricultural Development?," Asian Journal of Agriculture and Development, Southeast Asian Regional Center for Graduate Study and Research in Agriculture, vol. 7(1), pages 1-22, June.
  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.
  5. Robert Chambers & Rolf Färe, 2008. "A “calculus” for data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 30(3), pages 169-175, December.

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