Exchangeability hypothesis and initial premium feasibility in XLreinsurance with reinstatements

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.