term benefits and Business Expenses ), and the third reports results for Direct Life benefits 15 . Each part gives the results for no reinsurance, quota-share, quota-share and surplus, surplus and original reinsurance structure, which usually combines specified proportions of the others. The largest amount of premiums after paying all claims for short and long term benefits is retained under no reinsurance purchase as the expected value of reinsurance premiums exceeds the expected value of the reinsurance risk (e.g., reinsured claim amount) 16 . However the variance of total claims is significantly larger compared to the variances of the retained claims after any type of reinsurance is taken (see Figure 1). On average, the largest RPS ratio and the greatest amount of retained premiums from all reinsurance arrangements are obtained under a combination of quota-share and surplus (e.g., RPS = 3.8 and retained premium after claims = A $34.4 million.) making this cover optimal under profitability criteria. The smallest RPS ratio and retained premiums after claims are obtained under surplus reinsurance (e.g., RPS = 3.2 and retained premiums after claims = A $29.40 million.). This result is not surprising as the later cover is significantly more expensive compared with quota-share or quota- share and surplus covers (e.g., 90 percent of original premium for every A$1 reinsured under surplus compared to 70 percent of original premium for every A$1 reinsured under the other two arrangements). The smallest retained claim variance-to-mean ratio for short and long-term benefits is again obtained under a quota-share and surplus arrangement making this cover the optimal under the retained risk minimisation criteria. Benefits reinsured under quota-share reinsurance experience the largest retained claim variance compared with the other two reinsurance structures. This result confirms the
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