Levels of Determinism in Workers Compensation Reinsurance Commutations

When commuting workers compensation reinsurance claims, the standard method is to project the future value of the claims using stated assumptions for future medical usage, medical inflation, cost-of-living adjustments, and investment income. The actuary selects a best estimate for each variable, and assumes this deterministic number will be realized in the future. To account for the date of death being stochastic, a mortality table is used to model the future lifetime. By assuming deterministic values for future medical usage, medical inflation, cost-of-living adjustments, and investment income, the calculation ignores the possibilities of higher or lower values. It is shown that these do not generally balance out, and that the standard method produces biased results. In low reinsurance layers, the commutation amount is overstated, and in high layers it is understated. By removing deterministic assumptions from the calculation, bias is removed from the results. The paper gives a detailed, realistic, example to illustrate this. It is impossible to eliminate all determinism, but it is often appropriate to judgmentally adjust the answers to account for this. In discussing this, the paper draws parallels to the work of economists on “genuine uncertainty.” The implications of the paper reach beyond the narrow realm of workers compensation reinsurance commutations. The most obvious implications are for workers compensation reserving, but the essential message applies to pricing and reserving of any excess insurance and reinsurance: deterministic assumptions often lead to biased results.