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The Distorted Theory of Rank-Dependent Expected Utility

Author

Listed:
  • 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.

Suggested Citation

  • Hui Huang & Shunming Zhang, 2011. "The Distorted Theory of Rank-Dependent Expected Utility," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 233-263, November.
  • Handle: RePEc:cuf:journl:y:2011:v:12:i:2:p:233-263
    as

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    References listed on IDEAS

    as
    1. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December.
    2. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. 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, vol. 28(1), pages 175-202, February.
    5. Roell, Ailsa A, 1987. "Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 97(388a), pages 143-159, Supplemen.
    6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    7. 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, vol. 42(2), pages 370-381, August.
    8. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
    9. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    12. Segal, Uzi, 1987. "Some remarks on Quiggin's anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 8(1), pages 145-154, March.
    13. 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.
    14. 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.
    15. Quiggin, John, 1991. "Comparative Statics for Rank-Dependent Expected Utility Theory," Journal of Risk and Uncertainty, Springer, vol. 4(4), pages 339-350, December.
    16. 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, vol. 28(1), pages 229-240, February.
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    More about this item

    Keywords

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

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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