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XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis


Author Info

  • Paola Ferretti

    (Department of Economics, University Of Venice Cà Foscari)

  • Antonella Campana

    (Department of Economics, University Of Molise)


This paper studies excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution, in the framework of risk adjusted premium principle. By regarding to comonotonic exchangeability, a generalized definition of initial premium is proposed and some regularity properties characterizing it are presented, both with reference to conditions on underlying distortion functions both with respect to composing functions. The attention is then focused on conditions ensuring feasibility of generalized initial premiums with reference to the limit on the payment of each claim.

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Bibliographic Info

Paper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2011_14.

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Length: 15
Date of creation: 2011
Date of revision:
Handle: RePEc:ven:wpaper:2011_14

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Keywords: Excess of loss reinsurance; reinstatements; initial premium; exchangeability; distortion risk measures; feasibility.;

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  1. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
  2. Antonella Campana & Paola Ferretti, 2010. "Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements," Working Papers, Department of Applied Mathematics, Università Ca' Foscari Venezia 203, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
  4. Antonella Campana & Paola Ferretti, 2008. "What do distortion risk measures tell us on excess of loss reinsurance with reinstatements ?," Working Papers, Department of Applied Mathematics, Università Ca' Foscari Venezia 175, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  5. Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2004. "Some new classes of consistent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 505-516, June.
  6. Marc J. Goovaerts & Rob Kaas & Roger J.A. Laeven & Qihe Tang, 2004. "A Comonotonic Image of Independence for Additive Risk Measures," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-030/4, Tinbergen Institute.
  7. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
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