Actuarial claims costing, premium loading and claims reserving function
a(f_i, u_i, N, beta, gamma, sigma, P_m, c_d) = (C_bar, T, G, SD_N, I_m, U_m)
Maps utilisation rates, unit costs and the size of a covered group to the expected claims cost of a health insurance scheme, turns that expected cost into a gross premium or contribution with loadings, measures how predictable the group's average cost is, and estimates the claims incurred but not yet paid at a reporting date. These are the calculations of the Actuarial Analysis article. The plan generosity measure is covered separately on the Actuarial Value page.
Expected claims cost per covered person from utilisation and unit cost
C_bar = sum_(i=1)^k [f_i * u_i]; T = N * C_bar
Builds the expected claims cost per covered person per year service by service, as the sum over benefit categories of the utilisation rate times the unit cost, and multiplies it by the number of covered persons to give total expected claims for the year. The per-person cost is the net or risk premium for the group.
Gross health insurance premium from net premium with fixed and proportional loadings
G = (P + beta) / (1 - gamma)
Converts the net premium, the expected claims cost per covered person, into the gross annual premium by adding a fixed loading per person and a proportional loading set as a share of the gross premium. Because the proportional loading is a share of the result, the net premium plus the fixed loading is divided by one minus that share.
Standard deviation of the average claims cost in an insured pool
SD_N = sigma / sqrt(N)
Gives the standard deviation of the average annual claims cost per person across a pool of N people whose costs are independent with a common standard deviation. The spread of the average falls with the square root of the pool size, which is why large rating groups give reliable averages.
Incurred claims and unpaid claims from a completion factor
I_m = P_m / c_d; U_m = I_m - P_m
Estimates the total claims incurred for a month of service by dividing the amount paid so far by the completion factor, the cumulative share of a month's eventual claims that past experience shows to be paid by the same lag. The difference between estimated incurred and paid claims is the unpaid claims liability for that month, covering both unreported claims and claims reported but not yet paid.