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On Jensen's inequality for generalized Choquet integral with an application to risk aversion

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  • Wioletta Szeligowska
  • Marek Kaluszka

Abstract

In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk averse. Moreover, we show that the Arrow-Pratt theorem can be generalized to cover the case, where the expectation is replaced by the generalized Choquet integral.

Suggested Citation

  • Wioletta Szeligowska & Marek Kaluszka, 2016. "On Jensen's inequality for generalized Choquet integral with an application to risk aversion," Papers 1609.00554, arXiv.org.
  • Handle: RePEc:arx:papers:1609.00554
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    File URL: http://arxiv.org/pdf/1609.00554
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    References listed on IDEAS

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    1. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    2. 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.
    3. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    4. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    5. 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.
    6. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    7. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Mean-Value Principle under Cumulative Prospect Theory," ASTIN Bulletin, Cambridge University Press, vol. 42(1), pages 103-122, May.
    8. Georgescu, Irina, 2008. "Possibilistic Risk Aversion," Working Papers 476, IAMSR, Åbo Akademi.
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    1. repec:sgh:annals:i:51:y:2018:p:169-184 is not listed on IDEAS

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