Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 34 / 2 / Solution

For quota share reinsurance, each claim and therefore its aggregate are retained in the same proportion. For aggregate stop loss reinsurance, the insurer pays the aggregate up to the retention, and the reinsurer pays the excess. Thus the insurer's payouts areThe subscript $+$ denotes the positive part. The stop loss contract here applies to the annual aggregate, rather than separately to each claim.