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An alternative class of distortion operators

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  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Labex ReFi - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Bertrand Hassani

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Labex ReFi - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Kehan Li

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Labex ReFi - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

The distortion operator proposed by Wang (2000) has been developed in the actuarial literature and that are now part of the risk measurement tools inventory available for practitioners in finance and insurance. In this article, we propose an alternative class of distortion operators with explicit analytical inverse mapping. The distortion operators are based on tangent function allowing to transform a symmetrical unimodal distribution to an asymmetrical multimodal distribution.

Suggested Citation

  • Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "An alternative class of distortion operators," Post-Print halshs-01543251, HAL.
    • Handle: RePEc:hal:journl:halshs-01543251
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01543251
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    References listed on IDEAS

    as
    1. Dominique Guégan & Bertrand Hassani, 2015. "Distortion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 71-88, Springer.
    2. Bianchi, Marco, 1997. "Testing for Convergence: Evidence from Non-parametric Multimodality Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 393-409, July-Aug..
    3. Quah, Danny T, 1996. "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics," Economic Journal, Royal Economic Society, vol. 106(437), pages 1045-1055, July.
    4. Jong, Piet De & Marshall, Claymore, 2007. "Mortality Projection Based on the Wang Transform," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 149-161, May.
    5. Quah, Danny, 1997. "Empirics for growth and distribution," LSE Research Online Documents on Economics 2138, London School of Economics and Political Science, LSE Library.
    6. Feng Zhu, 2005. "A nonparametric analysis of the shape dynamics of the US personal income distribution: 1962-2000," BIS Working Papers 184, Bank for International Settlements.
    7. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    8. Quah, Danny, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," CEPR Discussion Papers 1586, C.E.P.R. Discussion Papers.
    9. 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.
    10. Charles I. Jones, 1997. "On the Evolution of the World Income Distribution," Journal of Economic Perspectives, American Economic Association, vol. 11(3), pages 19-36, Summer.
    11. Hamada, Mahmoud & Sherris, Michael & Hoek, John van der, 2006. "Dynamic Portfolio Allocation, the Dual Theory of Choice and Probability Distortion Functions," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 187-217, May.
    12. Danny Quah, 1996. "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics," CEP Discussion Papers dp0280, Centre for Economic Performance, LSE.
    13. Quah, Danny, 1996. "Twin peaks : growth and convergence in models of distribution dynamics," LSE Research Online Documents on Economics 2278, London School of Economics and Political Science, LSE Library.
    14. Danny Quah, 1997. "Empirics for Growth and Distribution," CEP Discussion Papers dp0324, Centre for Economic Performance, LSE.
    15. Mahmoud Hamada & Michael Sherris, 2003. "Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 19-47.
    16. Quah, Danny T., 1996. "Empirics for economic growth and convergence," European Economic Review, Elsevier, vol. 40(6), pages 1353-1375, June.
    17. Frédéric Godin & Silvia Mayoral & Manuel Morales, 2012. "Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 841-866, September.
    18. Quah, Danny T, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," Journal of Economic Growth, Springer, vol. 2(1), pages 27-59, March.
    19. Lynn Wirch, Julia & Hardy, Mary R., 1999. "A synthesis of risk measures for capital adequacy," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 337-347, December.
    20. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
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    Keywords

    Distortion operator; Multimodal distribution; Asymmetry; Invertibility;
    All these keywords.

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