IDEAS home Printed from
   My bibliography  Save this paper

On characterization of a class of convex operators for pricing insurance risks


  • Marta Cardin

    (Department of Applied Mathematics-University Ca'Foscari-Venice)

  • Graziella Pacelli

    (Department of Social sciences- University of Ancona)


The properties of risk measures or insurance premium principles have been extensively studied in actuarial literature. We propose an axiomatic description of a particular class of coherent risk measures defined in Artzner, Delbaen, Eber, and Heath (1999). The considered risk measures are obtained by expansion of TVar measures, consequently they look like very interesting in insurance pricing where TVar measures is frequently used to value tail risks.

Suggested Citation

  • Marta Cardin & Graziella Pacelli, 2005. "On characterization of a class of convex operators for pricing insurance risks," Game Theory and Information 0511011, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0511011
    Note: Type of Document - pdf; pages: 9

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    2. 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.
    3. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    4. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    5. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586,, revised Mar 2016.
    2. Schumacher Johannes M., 2018. "Distortion risk measures, ROC curves, and distortion divergence," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 35-50, January.
    3. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 767-800, December.
    4. Marta Cardin & Graziella Pacelli, 2008. "Characterization of Convex Premium Principles," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 53-60, Springer.
    5. Leitner, Johannes, 2005. "Dilatation monotonous Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 994-1006, December.
    6. Gabriela Zeller & Matthias Scherer, 2023. "Risk mitigation services in cyber insurance: optimal contract design and price structure," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 502-547, April.
    7. Mustapha Ridaoui & Michel Grabisch, 2016. "Choquet integral calculus on a continuous support and its applications," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(1), pages 73-93.
    8. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    9. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524.
    10. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    11. Monserrat Hernández-Solís & Cristina Lozano Colomer & José Luis Vilar Zanón., 2013. "El cálculo de la prima única de riesgo mediante la medida de riesgo transformada proporcional del tanto instantáneo," Economic Analysis Working Papers (2002-2010). Atlantic Review of Economics (2011-2016), Colexio de Economistas de A Coruña, Spain and Fundación Una Galicia Moderna, vol. 1, pages 1-1, June.
    12. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    13. Andreas Tsanakas & Evangelia Desli, 2005. "Measurement and Pricing of Risk in Insurance Markets," Risk Analysis, John Wiley & Sons, vol. 25(6), pages 1653-1668, December.
    14. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2021. "Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 302-319.
    15. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    16. Gzyl, Henryk & Mayoral, Silvia, 2008. "Determination of risk pricing measures from market prices of risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 437-443, December.
    17. Dilip mookerhjee, 2005. "New Directions in Development Economics: Theory or Empirics? - Is There Too Little Theory in Development Economics?," Boston University - Department of Economics - Working Papers Series WP2005-028, Boston University - Department of Economics.
    18. Samuel Solgon Santos & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2022. "The limitations of comonotonic additive risk measures: a literature review," Papers 2212.13864,, revised Jan 2024.
    19. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    20. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.

    More about this item


    Risk measures; premium principles; Choquet measures distortion function; TVar .;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0511011. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.