Community-rated premium, cross-subsidy and risk equalisation function
F(n_i, c_i, a, y, L_max) = (P, s_i, T_i, L)
Maps the number of members and the expected annual cost of each risk group in a community-rated pool to the single premium every member pays, the implicit cross-subsidy each group gives or receives, the risk equalisation transfers that offset those cross-subsidies for insurers, and the late-entry loadings that Ireland and Australia add to the premium of people who first buy cover when older. The same difference between payment and expected cost, read from the insurer's side, is the expected profit per member on the Cream Skimming page (HE-FM-CSKM-001).
Community-rated premium as the member-weighted mean expected cost
P = sum_(i=1)^I [n_i * c_i] / sum_(i=1)^I [n_i]
Under pure community rating every member of a pool pays the same premium, set at the average expected cost of the pool before any loading for administration and profit. Under adjusted community rating the same calculation applies within each permitted rating cell, such as an age band in a rating area. The premium is the mean of the risk groups' expected costs weighted by the number of members in each group.
Implicit cross-subsidy per member under community rating
s_i = P - c_i
The community-rated premium minus a member's expected cost. A positive value is the amount a member pays above expected cost towards others, as low-risk members do; a negative value is the amount by which a high-risk member's expected cost exceeds the premium. Weighted by the number of members, the cross-subsidies sum to zero across the pool, because the premium equals the pool's mean expected cost. Read from the insurer's side, the same quantity is the expected profit on that member in HE-FM-CSKM-001.
Risk equalisation transfer that offsets community-rating cross-subsidies
T_i = c_i - P
A payment from a central fund to an insurer for each member of risk group i, or from the insurer to the fund when negative, equal to the group's expected cost minus the community-rated premium. After the transfer each member brings the insurer an expected result of zero, because premium plus transfer equals expected cost. When the transfers use the same members and premium as the pool they sum to zero, so the fund balances. Van de Ven and colleagues report a consensus that removing the predictable over- and undercompensation of subgroups that community rating creates is part of the goal of risk equalisation.
Lifetime community rating late-entry loading
L = min(a * y, L_max); P_L = P_0 * (1 + L)
A percentage added to the community-rated premium of a person who first buys cover late, equal to a fixed rate for each counted year without cover up to a maximum. Ireland's Lifetime Community Rating, introduced from 1 May 2015, adds 2% of the gross premium for each year a person spent aged 35 or over without cover, up to a maximum of 70%; since a 2017 amendment the loading is withdrawn after 10 years of cover. Australia's Lifetime Health Cover, introduced on 1 July 2000, adds 2% for each year a person is over 30 when taking out hospital cover after the 1 July following their 31st birthday, up to 70%, and the loading stops after 10 years of continuous cover. The function min returns the smaller of its two arguments.