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An Iterativity Condition For The Mean-Value Principle Under Cumulative Prospect Theory

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  • Kaluszka, Marek
  • Krzeszowiec, Michał

Abstract

In this paper, we present the full characterization of the iterativity condition for the mean-value principle under the cumulative prospect theory. It turns out that the premium principle is iterative for exactly six pairs of probability distortion functions. Some of the corresponding premium principles are the classical mean-value principle, essential infimum or essential supremum of the random loss. Moreover, from the proof of the main theorem of this paper, it follows that the iterativity of the mean-value principle is equivalent to the iterativity of the generalized Choquet integral.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:43:y:2013:i:01:p:61-71_00
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    Cited by:

    1. 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.
    2. Wioletta Szeligowska & Marek Kaluszka, 2016. "On Jensen's inequality for generalized Choquet integral with an application to risk aversion," Papers 1609.00554, arXiv.org.
    3. Chudziak, J., 2018. "On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 243-246.
    4. Marek Kałuszka & Michał Krzeszowiec, 2013. "Iteracyjność składek ubezpieczeniowych w ujęciu teorii skumulowanej perspektywy i teorii nieokreśloności," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 45-56.

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