I have a question relating to the calculation of the reinsurer's share of UPR. For proportional insurance, this should be straightforward as a simple proportion of the gross UPR. However, for non-proportional reinsurance, how might this be calculated? If we assume that the direct insurance and reinsurance cover for a risk apply to the same period of exposure, then one simple answer would be that you use the same method of calculating unearned premium for the reinsurer as you do for the cedant (e.g. 1/365ths or something). However, it is complicated by the fact that, in the case of XoL, there may be reinstatement premiums. My thoughts are as follows. Suppose the cedant pays $1m in reinsurance premium for a risk on 1 January 2008 for a $10m xs $10m risk XoL layer. Suppose also that, 3 months later at 1 April 2008, there is a total loss to the layer. (Ignore reporting/settlement delays). Immediately prior to the loss, assuming uniform exposure to risk across the year, the unearned premium = 0.75 * $1m = $0.75m. Once the loss has occured, I would say that all the reinsurance premium has been earned, since there is no further exposure on the contract, without the payment of a reinstatement premium. Therefore, unearned premium = 0. Then, of the reinstatement premium that is to be paid, we calculate unearned premium as before, but this time our exposure period is just the remaining 9 months on the contract. I figure we can iterate like this until the contract expires at the end of the year, or all reinstatement premiums are used up, if sooner. Thoughts??
