surplus reinsurance leads to the smallest semi-variance of the retained claims.
The majority of TPD policies, 80%, were originally reinsured under surplus reinsurance, as such, the risk–return ratios for the original reinsurance structure are very close to those obtained under surplus reinsurance (see Fig. 3).
Both quota-share and the combination of quota-share and surplus reinsurance are sub optimal in managing TPD
risk, as these coverages lead to a semi-variance of the retained claims over five times higher than that under surplus reinsurance.