where r indexes the different proportional reinsurance arrangements
(quota-share, surplus, and combinations of quota-share and surplus).
Fig. 1 shows the distribution of the retained claim values for risk j.
The total number of claims is measured by nj, the individual retained claim
values are indicated by SIj , and the average value of all claims is denoted by E(SjI).
The variance of the retained claims accounts for both above and
below the mean variability, while semi-variance only accounts for the
variability above E(SjI)