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The Distorted Theory of Rank-Dependent Expected Utility

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  • Hui Huang

    (Faculty of Business Administration, University of Regina)

  • Shunming Zhang

    (China Financial Policy Research Center, Renmin University of China)

Abstract

This paper re-examines the rank-dependent expected utility theory. Firstly, we follow Quiggin's assumption (Quiggin 1982) to deduce the rank-dependent expected utility formula over lotteries and hence extend it to the case of general random variables. Secondly, we utilize the distortion function which reflects decision-makers' beliefs to propose a distorted independence axiom and then to prove the representation theorem of rank-dependent expected utility. Finally, we make direct use of the distorted independence axiom to explain the Allais paradox and the common ratio effect.

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Bibliographic Info

Article provided by Society for AEF in its journal Annals of Economics and Finance.

Volume (Year): 12 (2011)
Issue (Month): 2 (November)
Pages: 233-263

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Handle: RePEc:cuf:journl:y:2011:v:12:i:2:p:233-263

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Keywords: Expected utility; Rank-dependent expected utility; Distortion function; Distorted independence axiom; The Allais paradox; The Common ratio effect;

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  1. Uzi Segal, 1986. "Some Remarks on Quiggin's Anticipated Utility," UCLA Economics Working Papers, UCLA Department of Economics 392, UCLA Department of Economics.
  2. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
  3. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
  4. Quiggin, John, 1991. " Comparative Statics for Rank-Dependent Expected Utility Theory," Journal of Risk and Uncertainty, Springer, Springer, vol. 4(4), pages 339-50, December.
  5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 323-343, December.
  6. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, Elsevier, vol. 42(2), pages 370-381, August.
  7. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  8. Quiggin, J. & Wakker, P., 1992. "The Axiomatic Basis of Anticipated Utility : A Clarification," Discussion Paper, Tilburg University, Center for Economic Research 1992-3, Tilburg University, Center for Economic Research.
  9. Karni, Edi, 1987. "Generalized Expected Utility Analysis of Risk Aversion with State-Dependent Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 229-40, February.
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  11. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.
  12. Jianjun Miao, 2004. "A Note on Consumption and Savings under Knightian Uncertainty," Annals of Economics and Finance, Society for AEF, vol. 5(2), pages 299-311, November.
  13. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, Econometric Society, vol. 50(2), pages 277-323, March.
  14. Roell, Ailsa A, 1987. "Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 97(388a), pages 143-59, Supplemen.
  15. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 85(1), pages 97-122, February.
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