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A Simple Model of Cumulative Prospect Theory

Author

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  • U Schmidt
  • H Zank

Abstract

The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of cumulative prospect theory (CPT) in the framework for decision under uncertainty. We derive a two-sided variant of Choquet expected utility (CEU) with possibly different capacities for gains and for losses, and linear utility. Naturally, utility may have a kink at the status quo, which allows for the exhibition of loss aversion. The central condition of our model is termed independence of common increments.
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Suggested Citation

  • U Schmidt & H Zank, 2002. "A Simple Model of Cumulative Prospect Theory," Economics Discussion Paper Series 0206, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:0206
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    Cited by:

    1. James Cox & Vjollca Sadiraj & Ulrich Schmidt, 2015. "Paradoxes and mechanisms for choice under risk," Experimental Economics, Springer;Economic Science Association, vol. 18(2), pages 215-250, June.
    2. Bastianello, Lorenzo & Chateauneuf, Alain & Cornet, Bernard, 2024. "Gain–loss hedging and cumulative prospect theory," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 40-47.
    3. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    4. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    5. Olivier L'Haridon & Craig S. Webb & Horst Zank, 2021. "An Effective and Simple Tool for Measuring Loss Aversion," Economics Discussion Paper Series 2107, Economics, The University of Manchester.
    6. Schmidt, Ulrich & Zank, Horst, 2010. "Endogenizing prospect theory's reference point," Kiel Working Papers 1611, Kiel Institute for the World Economy (IfW Kiel).
    7. Wan, Shu-Ping & Li, Deng-Feng, 2013. "Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees," Omega, Elsevier, vol. 41(6), pages 925-940.
    8. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Han Bleichrodt & Ulrich Schmidt & Horst Zank, 2009. "Additive Utility in Prospect Theory," Management Science, INFORMS, vol. 55(5), pages 863-873, May.
    10. Glenn W. Harrison & J. Todd Swarthout, 2023. "Cumulative Prospect Theory in the Laboratory: A Reconsideration," Research in Experimental Economics, in: Models of Risk Preferences: Descriptive and Normative Challenges, volume 22, pages 107-192, Emerald Group Publishing Limited.
    11. Ulrich Schmidt & Horst Zank, 2007. "Linear cumulative prospect theory with applications to portfolio selection and insurance demand," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 30(1), pages 1-18, May.
    12. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.

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