Generalized initial premium in XL reinsurance 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. More precisely, after the attention is focused on conditions ensuring feasibility of initial premiums, for example concerning the limit on the payment of each claim, by regarding to comonotonic exchangeability a generalized definition of initial premium is set in the paper. Some regularity properties characterizing the proposed generalized initial premium are presented, both with reference to conditions on underlying distortion functions both with respect to composing function.