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What do distortion risk measures tell us on excess of loss reinsurance with reinstatements ?

Author

Listed:
  • Antonella Campana

    (Department SEGeS, University of Molise)

  • Paola Ferretti

    (Department of Applied Mathematics, University of Venice)

Abstract
In this paper we focused our attention to the study of an excess of loss reinsurance with reinstatements, a problem previously studied by Sundt [5] and, more recently, by Mata [4] and HÄurlimann [3]. As it is well-known, the evaluation of pure premiums requires the knowledge of the claim size distribution of the insurance risk: in order to face this question, different approaches have been followed in the actuarial literature. In a situation of incomplete information in which only some characteristics of the involved elements are known, it appears to be particularly interesting to set this problem in the framework of risk adjusted premiums. It is shown that if risk adjusted premiums satisfy a generalized expected value equation, then the initial premium exhibits some regularity properties as a function of the percentages of reinstatement.

Suggested Citation

  • Antonella Campana & Paola Ferretti, 2008. "What do distortion risk measures tell us on excess of loss reinsurance with reinstatements ?," Working Papers 175, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpaper:175
    as

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    File URL: http://virgo.unive.it/wpideas/storage/2008wp175.pdf
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    References listed on IDEAS

    as
    1. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    2. Mata, Ana J., 2000. "Pricing Excess of Loss Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 349-368, November.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Paola Ferretti & Antonella Campana, 2011. "XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis," Working Papers 2011_14, Department of Economics, University of Venice "Ca' Foscari".

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    More about this item

    Keywords

    Excess of loss reinsurance; reinstatements; distortion risk measures; expected value equation;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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