Consider a life insurer with a portfolio of nj risks where j indexes the
different policy type (e.g., Trauma, Income Protection). The insurance
policy, which covers one risk, is indexed by ij and is characterized by
its risk exposure (e.g., the sum insured value) SIi j, premiumPi j , and individual
loss or claimSi j. In the case of no reinsurance, the insurer retains
all the risk exposure (SIj), premium (Pj), and it pays the full loss (Sj):