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On iterative premium calculation principles under Cumulative Prospect Theory

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  • Kaluszka, Marek
  • Krzeszowiec, Michał

Abstract

In the paper we analyze the iterativity condition for zero utility principle adjusted to Cumulative Prospect Theory. We prove, under mild conditions, that the premium principle is iterative if and only if the value function is linear or exponential and probability distortion functions are identities, i.e. the probabilities are not distorted.

Suggested Citation

  • Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 435-440.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:435-440
    DOI: 10.1016/j.insmatheco.2013.02.009
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    References listed on IDEAS

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    1. Goovaerts, M. J. & Vylder, F. De, 1979. "A Note on Iterative Premium Calculation Principles," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 325-329, December.
    2. 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.
    3. Heilpern, S., 2003. "A rank-dependent generalization of zero utility principle," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 67-73, August.
    4. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
    5. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
    6. van der Hoek, John & Sherris, Michael, 2001. "A class of non-expected utility risk measures and implications for asset allocations," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 69-82, February.
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    Citations

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    Cited by:

    1. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    2. Martina Nardon & Paolo Pianca, 2019. "Insurance premium calculation under continuous cumulative prospect theory," Working Papers 2019:03, Department of Economics, University of Venice "Ca' Foscari".
    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. Mitja Stadje, 2018. "Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing," Papers 1811.09615, arXiv.org, revised Dec 2018.
    5. Chudziak, J., 2020. "On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 154-159.
    6. 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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    More about this item

    Keywords

    Cumulative Prospect Theory; Iterativity; Zero utility principle; Non-expected utility; Generalized Choquet integral;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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