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On the Arrow-Pratt risk aversion model for the generalized Choquet integral

Author

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  • Marek Kałuszka

    (Politechnika Łódzka, Wydział Fizyki Technicznej, Informatyki i Matematyki Stosowanej)

  • Wioletta Szeligowska

    (Politechnika Łódzka, Wydział Fizyki Technicznej, Informatyki i Matematyki Stosowanej)

Abstract

In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people do not behave accordingly to the von Neumann-Morgenstern’s Expected Utility Theory. Therefore, they proposed an alternative theory, called the Cumulative Prospect Theory, in which they used the Choquet integral with respect to distorted probability measures to describe decision making in risk and uncertainty conditions. The paper presents the generalized Arrow-Pratt risk aversion model, when the classic expected value is replaced by the generalized Choquet integral. To do this, we require necessary and sufficient conditions for the Jensen type inequality for the generalized Choquet integral with respect to arbitrary monotone measure, that is not an additive set function. We will provide some results of this type and point the difficulties that show up without the additivity assumption.

Suggested Citation

  • Marek Kałuszka & Wioletta Szeligowska, 2018. "On the Arrow-Pratt risk aversion model for the generalized Choquet integral," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 169-184.
    • Handle: RePEc:sgh:annals:i:51:y:2018:p:169-184
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    References listed on IDEAS

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    1. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "An Iterativity Condition For The Mean-Value Principle Under Cumulative Prospect Theory," ASTIN Bulletin, Cambridge University Press, vol. 43(1), pages 61-71, January.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Mean-Value Principle under Cumulative Prospect Theory," ASTIN Bulletin, Cambridge University Press, vol. 42(1), pages 103-122, May.
    5. Jian Zhou & Yuanyuan Liu & Xiaoxia Zhang & Xin Gu & Di Wang, 2017. "Uncertain risk aversion," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 615-624, March.
    6. Wioletta Szeligowska & Marek Kaluszka, 2016. "On Jensen's inequality for generalized Choquet integral with an application to risk aversion," Papers 1609.00554, arXiv.org.
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