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Iterated Expectations under Cumulative Prospect Theory: an Impossibility Result

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  • Alex Stomper

    ()
    (Humboldt University)

  • Marie-Louise Vierø

    ()
    (Queen's University)

Abstract

Under expected utility theory, compound lotteries can be valued by "iterating" expectations: the expected utility of a compound lottery is the expected value of a simple lottery over prizes that are certainty equivalents to follow-up lotteries. We derive necessary and sufficient conditions for a similar valuation technique in the framework of Cumulative Prospect Theory (CPT) when a decision maker has to choose between prospects that belong to a comonotonic class. Our conditions characterize the compatibility of a prominent alternative to expected utility with valuation methods that are commonly used in applied economics and finance, e.g. in binomial option pricing. The conditions can be viewed as an impossibility result.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1228.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1228.

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Length: 20 pages
Date of creation: May 2014
Date of revision:
Handle: RePEc:qed:wpaper:1228

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Keywords: Cumulative Prospect Theory; probability weighting function; conditioning; updating; dynamic consistency; model consistency; consequentialism; valuation methods; Iterated expectations;

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References

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  1. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  2. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  3. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-50, July-Aug..
  4. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  5. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
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