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Distortion Risk Measures and Discrete Risks

Author

Listed:
  • Antonella Campana

    (Department SEGeS - University of Molise)

  • Paola Ferretti

    (Department of Applied Mathematics - University Ca' Foscari)

Abstract

In this paper we consider the problem of determining approximations for distortion risk measures of sums of non-independent random variables. First, we give an overview of the recent actuarial literature on distortion risk measures and convex bounds for sums of random variables. Then, we examine the case of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. The result is then extended to cover the case of non necessarily discrete risks.

Suggested Citation

  • Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0510013
    Note: Type of Document - pdf; pages: 13
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0510/0510013.pdf
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    References listed on IDEAS

    as
    1. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    3. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    4. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    5. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    6. 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.
    7. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Antonella Campana & Paola Ferretti, 2008. "Bounds for Concave Distortion Risk Measures for Sums of Risks," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 43-51, Springer.
    2. Ragnar Levy Gudmundarson & Manuel Guerra & Alexandra Bugalho de Moura, 2021. "Minimizing ruin probability under dependencies for insurance pricing," Papers 2108.10075, arXiv.org.
    3. R.L. Gudmundarson & M. Guerra & A. B. de Moura, 2021. "Minimizing Ruin Probability Under Dependencies for Insurance Pricing," Working Papers REM 2021/0193, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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    More about this item

    Keywords

    Risk measures; dependency of risks; discrete risks with identical distribution; upper and lower bounds: concave risk measures.;
    All these keywords.

    JEL classification:

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

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