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Dual Approaches to the Analysis of Risk Aversion

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Author Info
ROBERT G. CHAMBERS
JOHN QUIGGIN

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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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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-0335.2006.00535.x
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Publisher 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. 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. [Downloadable!] (restricted)
  2. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481. [Downloadable!] (restricted)
  3. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August. [Downloadable!] (restricted)
  4. Milne, Frank, 1979. "Consumer Preferences, Linear Demand Functions and Aggregation in Competitive Asset Markets," Review of Economic Studies, Blackwell Publishing, vol. 46(3), pages 407-17, July. [Downloadable!] (restricted)
  5. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November. [Downloadable!] (restricted)
  12. Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics. [Downloadable!]
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  13. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer, vol. 11(3), pages 629-641. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
  15. Peleg, Bezalel, 1975. "Efficient random variables," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 243-252. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  1. Robert Chambers & Rolf Färe, 2008. "A “calculus” for data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 30(3), pages 169-175, December. [Downloadable!] (restricted)
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