XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis
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.
|Date of creation:||2011|
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- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- 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.
- Antonella Campana & Paola Ferretti, 2010. "Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements," Working Papers 203, Department of Applied Mathematics, Università Ca' Foscari Venezia.
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- 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.
- 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.
- 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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